Daily Papers

Large language models (LLMs) can improve their accuracy on various tasks through iteratively refining and revising their output based on feedback. We observe that these revisions can introduce errors, in which case it is better to roll back to a previous result. Further, revisions are typically homogeneous: they use the same reasoning method that produced the initial answer, which may not correct errors. To enable exploration in this space, we present SCREWS, a modular framework for reasoning with revisions. It is comprised of three main modules: Sampling, Conditional Resampling, and Selection, each consisting of sub-modules that can be hand-selected per task. We show that SCREWS not only unifies several previous approaches under a common framework, but also reveals several novel strategies for identifying improved reasoning chains. We evaluate our framework with state-of-the-art LLMs (ChatGPT and GPT-4) on a diverse set of reasoning tasks and uncover useful new reasoning strategies for each: arithmetic word problems, multi-hop question answering, and code debugging. Heterogeneous revision strategies prove to be important, as does selection between original and revised candidates.

Conditional contrastive learning frameworks consider the conditional sampling procedure that constructs positive or negative data pairs conditioned on specific variables. Fair contrastive learning constructs negative pairs, for example, from the same gender (conditioning on sensitive information), which in turn reduces undesirable information from the learned representations; weakly supervised contrastive learning constructs positive pairs with similar annotative attributes (conditioning on auxiliary information), which in turn are incorporated into the representations. Although conditional contrastive learning enables many applications, the conditional sampling procedure can be challenging if we cannot obtain sufficient data pairs for some values of the conditioning variable. This paper presents Conditional Contrastive Learning with Kernel (CCL-K) that converts existing conditional contrastive objectives into alternative forms that mitigate the insufficient data problem. Instead of sampling data according to the value of the conditioning variable, CCL-K uses the Kernel Conditional Embedding Operator that samples data from all available data and assigns weights to each sampled data given the kernel similarity between the values of the conditioning variable. We conduct experiments using weakly supervised, fair, and hard negatives contrastive learning, showing CCL-K outperforms state-of-the-art baselines.

While conditional diffusion models are known to have good coverage of the data distribution, they still face limitations in output diversity, particularly when sampled with a high classifier-free guidance scale for optimal image quality or when trained on small datasets. We attribute this problem to the role of the conditioning signal in inference and offer an improved sampling strategy for diffusion models that can increase generation diversity, especially at high guidance scales, with minimal loss of sample quality. Our sampling strategy anneals the conditioning signal by adding scheduled, monotonically decreasing Gaussian noise to the conditioning vector during inference to balance diversity and condition alignment. Our Condition-Annealed Diffusion Sampler (CADS) can be used with any pretrained model and sampling algorithm, and we show that it boosts the diversity of diffusion models in various conditional generation tasks. Further, using an existing pretrained diffusion model, CADS achieves a new state-of-the-art FID of 1.70 and 2.31 for class-conditional ImageNet generation at 256times256 and 512times512 respectively.

Reconstruction of magnetic resonance imaging (MRI) data has been positively affected by deep learning. A key challenge remains: to improve generalisation to distribution shifts between the training and testing data. Most approaches aim to address this via inductive design or data augmentation. However, they can be affected by misleading data, e.g. random noise, and cases where the inference stage data do not match assumptions in the modelled shifts. In this work, by employing a conditional hyperparameter network, we eliminate the need of augmentation, yet maintain robust performance under various levels of Gaussian noise. We demonstrate that our model withstands various input noise levels while producing high-definition reconstructions during the test stage. Moreover, we present a hyperparameter sampling strategy that accelerates the convergence of training. Our proposed method achieves the highest accuracy and image quality in all settings compared to baseline methods.

We propose Conditional Adapter (CoDA), a parameter-efficient transfer learning method that also improves inference efficiency. CoDA generalizes beyond standard adapter approaches to enable a new way of balancing speed and accuracy using conditional computation. Starting with an existing dense pretrained model, CoDA adds sparse activation together with a small number of new parameters and a light-weight training phase. Our experiments demonstrate that the CoDA approach provides an unexpectedly efficient way to transfer knowledge. Across a variety of language, vision, and speech tasks, CoDA achieves a 2x to 8x inference speed-up compared to the state-of-the-art Adapter approaches with moderate to no accuracy loss and the same parameter efficiency.

We demonstrate how conditional generation from diffusion models can be used to tackle a variety of realistic tasks in the production of music in 44.1kHz stereo audio with sampling-time guidance. The scenarios we consider include continuation, inpainting and regeneration of musical audio, the creation of smooth transitions between two different music tracks, and the transfer of desired stylistic characteristics to existing audio clips. We achieve this by applying guidance at sampling time in a simple framework that supports both reconstruction and classification losses, or any combination of the two. This approach ensures that generated audio can match its surrounding context, or conform to a class distribution or latent representation specified relative to any suitable pre-trained classifier or embedding model.

Reliable machine learning and statistical analysis rely on diverse, well-distributed training data. However, real-world datasets are often limited in size and exhibit underrepresentation across key subpopulations, leading to biased predictions and reduced performance, particularly in supervised tasks such as classification. To address these challenges, we propose Conditional Data Synthesis Augmentation (CoDSA), a novel framework that leverages generative models, such as diffusion models, to synthesize high-fidelity data for improving model performance across multimodal domains including tabular, textual, and image data. CoDSA generates synthetic samples that faithfully capture the conditional distributions of the original data, with a focus on under-sampled or high-interest regions. Through transfer learning, CoDSA fine-tunes pre-trained generative models to enhance the realism of synthetic data and increase sample density in sparse areas. This process preserves inter-modal relationships, mitigates data imbalance, improves domain adaptation, and boosts generalization. We also introduce a theoretical framework that quantifies the statistical accuracy improvements enabled by CoDSA as a function of synthetic sample volume and targeted region allocation, providing formal guarantees of its effectiveness. Extensive experiments demonstrate that CoDSA consistently outperforms non-adaptive augmentation strategies and state-of-the-art baselines in both supervised and unsupervised settings.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the ability of graphical models to compactly model multivariate data with the ability of classification methods to perform prediction using large sets of input features. This tutorial describes conditional random fields, a popular probabilistic method for structured prediction. CRFs have seen wide application in natural language processing, computer vision, and bioinformatics. We describe methods for inference and parameter estimation for CRFs, including practical issues for implementing large scale CRFs. We do not assume previous knowledge of graphical modeling, so this tutorial is intended to be useful to practitioners in a wide variety of fields.

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.

Pixel-wise predictions are required in a wide variety of tasks such as image restoration, image segmentation, or disparity estimation. Common models involve several stages of data resampling, in which the resolution of feature maps is first reduced to aggregate information and then increased to generate a high-resolution output. Previous works have shown that resampling operations are subject to artifacts such as aliasing. During downsampling, aliases have been shown to compromise the prediction stability of image classifiers. During upsampling, they have been leveraged to detect generated content. Yet, the effect of aliases during upsampling has not yet been discussed w.r.t. the stability and robustness of pixel-wise predictions. While falling under the same term (aliasing), the challenges for correct upsampling in neural networks differ significantly from those during downsampling: when downsampling, some high frequencies can not be correctly represented and have to be removed to avoid aliases. However, when upsampling for pixel-wise predictions, we actually require the model to restore such high frequencies that can not be encoded in lower resolutions. The application of findings from signal processing is therefore a necessary but not a sufficient condition to achieve the desirable output. In contrast, we find that the availability of large spatial context during upsampling allows to provide stable, high-quality pixel-wise predictions, even when fully learning all filter weights.

Recent progress in image generation has sparked research into controlling these models through condition signals, with various methods addressing specific challenges in conditional generation. Instead of proposing another specialized technique, we introduce a simple, unified framework to handle diverse conditional generation tasks involving a specific image-condition correlation. By learning a joint distribution over a correlated image pair (e.g. image and depth) with a diffusion model, our approach enables versatile capabilities via different inference-time sampling schemes, including controllable image generation (e.g. depth to image), estimation (e.g. image to depth), signal guidance, joint generation (image & depth), and coarse control. Previous attempts at unification often introduce significant complexity through multi-stage training, architectural modification, or increased parameter counts. In contrast, our simple formulation requires a single, computationally efficient training stage, maintains the standard model input, and adds minimal learned parameters (15% of the base model). Moreover, our model supports additional capabilities like non-spatially aligned and coarse conditioning. Extensive results show that our single model can produce comparable results with specialized methods and better results than prior unified methods. We also demonstrate that multiple models can be effectively combined for multi-signal conditional generation.

This paper introduces WaveGrad, a conditional model for waveform generation which estimates gradients of the data density. The model is built on prior work on score matching and diffusion probabilistic models. It starts from a Gaussian white noise signal and iteratively refines the signal via a gradient-based sampler conditioned on the mel-spectrogram. WaveGrad offers a natural way to trade inference speed for sample quality by adjusting the number of refinement steps, and bridges the gap between non-autoregressive and autoregressive models in terms of audio quality. We find that it can generate high fidelity audio samples using as few as six iterations. Experiments reveal WaveGrad to generate high fidelity audio, outperforming adversarial non-autoregressive baselines and matching a strong likelihood-based autoregressive baseline using fewer sequential operations. Audio samples are available at https://wavegrad.github.io/.

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.

Transductive Few-Shot Learning (TFSL) has recently attracted increasing attention since it typically outperforms its inductive peer by leveraging statistics of query samples. However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called {\textbf P}rototypes-oriented {\textbf U}nbiased {\textbf T}ransfer {\textbf M}odel (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization.

We propose TR0N, a highly general framework to turn pre-trained unconditional generative models, such as GANs and VAEs, into conditional models. The conditioning can be highly arbitrary, and requires only a pre-trained auxiliary model. For example, we show how to turn unconditional models into class-conditional ones with the help of a classifier, and also into text-to-image models by leveraging CLIP. TR0N learns a lightweight stochastic mapping which "translates" between the space of conditions and the latent space of the generative model, in such a way that the generated latent corresponds to a data sample satisfying the desired condition. The translated latent samples are then further improved upon through Langevin dynamics, enabling us to obtain higher-quality data samples. TR0N requires no training data nor fine-tuning, yet can achieve a zero-shot FID of 10.9 on MS-COCO, outperforming competing alternatives not only on this metric, but also in sampling speed -- all while retaining a much higher level of generality. Our code is available at https://github.com/layer6ai-labs/tr0n.

JPEG is arguably the most popular image coding format, achieving high compression ratios via lossy quantization that may create visual artifacts degradation. Numerous attempts to remove these artifacts were conceived over the years, and common to most of these is the use of deterministic post-processing algorithms that optimize some distortion measure (e.g., PSNR, SSIM). In this paper we propose a different paradigm for JPEG artifact correction: Our method is stochastic, and the objective we target is high perceptual quality -- striving to obtain sharp, detailed and visually pleasing reconstructed images, while being consistent with the compressed input. These goals are achieved by training a stochastic conditional generator (conditioned on the compressed input), accompanied by a theoretically well-founded loss term, resulting in a sampler from the posterior distribution. Our solution offers a diverse set of plausible and fast reconstructions for a given input with perfect consistency. We demonstrate our scheme's unique properties and its superiority to a variety of alternative methods on the FFHQ and ImageNet datasets.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

We consider the problem of weakly supervised object detection, where the training samples are annotated using only image-level labels that indicate the presence or absence of an object category. In order to model the uncertainty in the location of the objects, we employ a dissimilarity coefficient based probabilistic learning objective. The learning objective minimizes the difference between an annotation agnostic prediction distribution and an annotation aware conditional distribution. The main computational challenge is the complex nature of the conditional distribution, which consists of terms over hundreds or thousands of variables. The complexity of the conditional distribution rules out the possibility of explicitly modeling it. Instead, we exploit the fact that deep learning frameworks rely on stochastic optimization. This allows us to use a state of the art discrete generative model that can provide annotation consistent samples from the conditional distribution. Extensive experiments on PASCAL VOC 2007 and 2012 data sets demonstrate the efficacy of our proposed approach.

Neural Posterior Estimation methods for simulation-based inference can be ill-suited for dealing with posterior distributions obtained by conditioning on multiple observations, as they tend to require a large number of simulator calls to learn accurate approximations. In contrast, Neural Likelihood Estimation methods can handle multiple observations at inference time after learning from individual observations, but they rely on standard inference methods, such as MCMC or variational inference, which come with certain performance drawbacks. We introduce a new method based on conditional score modeling that enjoys the benefits of both approaches. We model the scores of the (diffused) posterior distributions induced by individual observations, and introduce a way of combining the learned scores to approximately sample from the target posterior distribution. Our approach is sample-efficient, can naturally aggregate multiple observations at inference time, and avoids the drawbacks of standard inference methods.

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition time by collecting data below the Nyquist rate. As an ill-posed inverse problem, many plausible solutions exist, yet the majority of deep learning approaches generate only a single solution. We instead focus on sampling from the posterior distribution, which provides more comprehensive information for downstream inference tasks. To do this, we design a novel conditional normalizing flow (CNF) that infers the signal component in the measurement operator's nullspace, which is later combined with measured data to form complete images. Using fastMRI brain and knee data, we demonstrate fast inference and accuracy that surpasses recent posterior sampling techniques for MRI. Code is available at https://github.com/jwen307/mri_cnf/

We introduce a novel approach to counter adversarial attacks, namely, image resampling. Image resampling transforms a discrete image into a new one, simulating the process of scene recapturing or rerendering as specified by a geometrical transformation. The underlying rationale behind our idea is that image resampling can alleviate the influence of adversarial perturbations while preserving essential semantic information, thereby conferring an inherent advantage in defending against adversarial attacks. To validate this concept, we present a comprehensive study on leveraging image resampling to defend against adversarial attacks. We have developed basic resampling methods that employ interpolation strategies and coordinate shifting magnitudes. Our analysis reveals that these basic methods can partially mitigate adversarial attacks. However, they come with apparent limitations: the accuracy of clean images noticeably decreases, while the improvement in accuracy on adversarial examples is not substantial. We propose implicit representation-driven image resampling (IRAD) to overcome these limitations. First, we construct an implicit continuous representation that enables us to represent any input image within a continuous coordinate space. Second, we introduce SampleNet, which automatically generates pixel-wise shifts for resampling in response to different inputs. Furthermore, we can extend our approach to the state-of-the-art diffusion-based method, accelerating it with fewer time steps while preserving its defense capability. Extensive experiments demonstrate that our method significantly enhances the adversarial robustness of diverse deep models against various attacks while maintaining high accuracy on clean images.

In generative models, two paradigms have gained attraction in various applications: next-set prediction-based Masked Generative Models and next-noise prediction-based Non-Autoregressive Models, e.g., Diffusion Models. In this work, we propose using discrete-state models to connect them and explore their scalability in the vision domain. First, we conduct a step-by-step analysis in a unified design space across two types of models including timestep-independence, noise schedule, temperature, guidance strength, etc in a scalable manner. Second, we re-cast typical discriminative tasks, e.g., image segmentation, as an unmasking process from [MASK]tokens on a discrete-state model. This enables us to perform various sampling processes, including flexible conditional sampling by only training once to model the joint distribution. All aforementioned explorations lead to our framework named Discrete Interpolants, which enables us to achieve state-of-the-art or competitive performance compared to previous discrete-state based methods in various benchmarks, like ImageNet256, MS COCO, and video dataset FaceForensics. In summary, by leveraging [MASK] in discrete-state models, we can bridge Masked Generative and Non-autoregressive Diffusion models, as well as generative and discriminative tasks.

For learning with noisy labels, the transition matrix, which explicitly models the relation between noisy label distribution and clean label distribution, has been utilized to achieve the statistical consistency of either the classifier or the risk. Previous researches have focused more on how to estimate this transition matrix well, rather than how to utilize it. We propose good utilization of the transition matrix is crucial and suggest a new utilization method based on resampling, coined RENT. Specifically, we first demonstrate current utilizations can have potential limitations for implementation. As an extension to Reweighting, we suggest the Dirichlet distribution-based per-sample Weight Sampling (DWS) framework, and compare reweighting and resampling under DWS framework. With the analyses from DWS, we propose RENT, a REsampling method with Noise Transition matrix. Empirically, RENT consistently outperforms existing transition matrix utilization methods, which includes reweighting, on various benchmark datasets. Our code is available at https://github.com/BaeHeeSun/RENT.

Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity problem in regression, existing conditional distribution alignment theory and methods with discrete prior, which are proven to be effective in classification settings, are no longer applicable. In this work, focusing on the feasibility problems in DAR, we establish the sufficiency theory for the regression model, which shows the generalization error can be sufficiently dominated by the cross-domain conditional discrepancy. Further, to characterize conditional discrepancy with continuous conditioning variable, a novel Conditional Operator Discrepancy (COD) is proposed, which admits the metric property on conditional distributions via the kernel embedding theory. Finally, to minimize the discrepancy, a COD-based conditional invariant representation learning model is proposed, and the reformulation is derived to show that reasonable modifications on moment statistics can further improve the discriminability of the adaptation model. Extensive experiments on standard DAR datasets verify the validity of theoretical results and the superiority over SOTA DAR methods.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

Over the last decade, the process of automatic image colorization has been of significant interest for several application areas including restoration of aged or degraded images. This problem is highly ill-posed due to the large degrees of freedom during the assignment of color information. Many of the recent developments in automatic colorization involve images that contain a common theme or require highly processed data such as semantic maps as input. In our approach, we attempt to fully generalize the colorization procedure using a conditional Deep Convolutional Generative Adversarial Network (DCGAN), extend current methods to high-resolution images and suggest training strategies that speed up the process and greatly stabilize it. The network is trained over datasets that are publicly available such as CIFAR-10 and Places365. The results of the generative model and traditional deep neural networks are compared.

Conditional normalizing flows can generate diverse image samples for solving inverse problems. Most normalizing flows for inverse problems in imaging employ the conditional affine coupling layer that can generate diverse images quickly. However, unintended severe artifacts are occasionally observed in the output of them. In this work, we address this critical issue by investigating the origins of these artifacts and proposing the conditions to avoid them. First of all, we empirically and theoretically reveal that these problems are caused by "exploding inverse" in the conditional affine coupling layer for certain out-of-distribution (OOD) conditional inputs. Then, we further validated that the probability of causing erroneous artifacts in pixels is highly correlated with a Mahalanobis distance-based OOD score for inverse problems in imaging. Lastly, based on our investigations, we propose a remark to avoid exploding inverse and then based on it, we suggest a simple remedy that substitutes the affine coupling layers with the modified rational quadratic spline coupling layers in normalizing flows, to encourage the robustness of generated image samples. Our experimental results demonstrated that our suggested methods effectively suppressed critical artifacts occurring in normalizing flows for super-resolution space generation and low-light image enhancement.

Solving Bayesian inverse problems efficiently remains a significant challenge due to the complexity of posterior distributions and the computational cost of traditional sampling methods. Given a series of observations and the forward model, we want to recover the distribution of the parameters, conditioned on observed experimental data. We show, that combining Conditional Flow Mathching (CFM) with transformer-based architecture, we can efficiently sample from such kind of distribution, conditioned on variable number of observations.

Diffusion probabilistic models (DPMs) have become a popular approach to conditional generation, due to their promising results and support for cross-modal synthesis. A key desideratum in conditional synthesis is to achieve high correspondence between the conditioning input and generated output. Most existing methods learn such relationships implicitly, by incorporating the prior into the variational lower bound. In this work, we take a different route -- we explicitly enhance input-output connections by maximizing their mutual information. To this end, we introduce a Conditional Discrete Contrastive Diffusion (CDCD) loss and design two contrastive diffusion mechanisms to effectively incorporate it into the denoising process, combining the diffusion training and contrastive learning for the first time by connecting it with the conventional variational objectives. We demonstrate the efficacy of our approach in evaluations with diverse multimodal conditional synthesis tasks: dance-to-music generation, text-to-image synthesis, as well as class-conditioned image synthesis. On each, we enhance the input-output correspondence and achieve higher or competitive general synthesis quality. Furthermore, the proposed approach improves the convergence of diffusion models, reducing the number of required diffusion steps by more than 35% on two benchmarks, significantly increasing the inference speed.

Generative Adversarial Nets [8] were recently introduced as a novel way to train generative models. In this work we introduce the conditional version of generative adversarial nets, which can be constructed by simply feeding the data, y, we wish to condition on to both the generator and discriminator. We show that this model can generate MNIST digits conditioned on class labels. We also illustrate how this model could be used to learn a multi-modal model, and provide preliminary examples of an application to image tagging in which we demonstrate how this approach can generate descriptive tags which are not part of training labels.

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images -- the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or misspecified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates x) of training and testing samples p_tr(x) and p_te(x) are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio p_te(x)/p_tr(x) to weight training samples (reweighted methods) or using the ratio p_tr(x)/p_te(x) to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

Pan-sharpening aims to generate a high-resolution multispectral (HRMS) image by integrating the spectral information of a low-resolution multispectral (LRMS) image with the texture details of a high-resolution panchromatic (PAN) image. It essentially inherits the ill-posed nature of the super-resolution (SR) task that diverse HRMS images can degrade into an LRMS image. However, existing deep learning-based methods recover only one HRMS image from the LRMS image and PAN image using a deterministic mapping, thus ignoring the diversity of the HRMS image. In this paper, to alleviate this ill-posed issue, we propose a flow-based pan-sharpening network (PanFlowNet) to directly learn the conditional distribution of HRMS image given LRMS image and PAN image instead of learning a deterministic mapping. Specifically, we first transform this unknown conditional distribution into a given Gaussian distribution by an invertible network, and the conditional distribution can thus be explicitly defined. Then, we design an invertible Conditional Affine Coupling Block (CACB) and further build the architecture of PanFlowNet by stacking a series of CACBs. Finally, the PanFlowNet is trained by maximizing the log-likelihood of the conditional distribution given a training set and can then be used to predict diverse HRMS images. The experimental results verify that the proposed PanFlowNet can generate various HRMS images given an LRMS image and a PAN image. Additionally, the experimental results on different kinds of satellite datasets also demonstrate the superiority of our PanFlowNet compared with other state-of-the-art methods both visually and quantitatively.

To measure the difference between two probability distributions, referred to as the source and target, respectively, we exploit both the chain rule and Bayes' theorem to construct conditional transport (CT), which is constituted by both a forward component and a backward one. The forward CT is the expected cost of moving a source data point to a target one, with their joint distribution defined by the product of the source probability density function (PDF) and a source-dependent conditional distribution, which is related to the target PDF via Bayes' theorem. The backward CT is defined by reversing the direction. The CT cost can be approximated by replacing the source and target PDFs with their discrete empirical distributions supported on mini-batches, making it amenable to implicit distributions and stochastic gradient descent-based optimization. When applied to train a generative model, CT is shown to strike a good balance between mode-covering and mode-seeking behaviors and strongly resist mode collapse. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing generative adversarial network with CT is shown to consistently improve the performance. PyTorch code is provided.

Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only combining examples across classes or domains. These methods have claimed remarkable improvements on benchmarks with distribution shifts, but their mechanisms and limitations remain poorly understood. We examine an overlooked aspect of selective mixup that explains its success in a completely new light. We find that the non-random selection of pairs affects the training distribution and improve generalization by means completely unrelated to the mixing. For example in binary classification, mixup across classes implicitly resamples the data for a uniform class distribution - a classical solution to label shift. We show empirically that this implicit resampling explains much of the improvements in prior work. Theoretically, these results rely on a regression toward the mean, an accidental property that we identify in several datasets. We have found a new equivalence between two successful methods: selective mixup and resampling. We identify limits of the former, confirm the effectiveness of the latter, and find better combinations of their respective benefits.

In object detection, an intersection over union (IoU) threshold is required to define positives and negatives. An object detector, trained with low IoU threshold, e.g. 0.5, usually produces noisy detections. However, detection performance tends to degrade with increasing the IoU thresholds. Two main factors are responsible for this: 1) overfitting during training, due to exponentially vanishing positive samples, and 2) inference-time mismatch between the IoUs for which the detector is optimal and those of the input hypotheses. A multi-stage object detection architecture, the Cascade R-CNN, is proposed to address these problems. It consists of a sequence of detectors trained with increasing IoU thresholds, to be sequentially more selective against close false positives. The detectors are trained stage by stage, leveraging the observation that the output of a detector is a good distribution for training the next higher quality detector. The resampling of progressively improved hypotheses guarantees that all detectors have a positive set of examples of equivalent size, reducing the overfitting problem. The same cascade procedure is applied at inference, enabling a closer match between the hypotheses and the detector quality of each stage. A simple implementation of the Cascade R-CNN is shown to surpass all single-model object detectors on the challenging COCO dataset. Experiments also show that the Cascade R-CNN is widely applicable across detector architectures, achieving consistent gains independently of the baseline detector strength. The code will be made available at https://github.com/zhaoweicai/cascade-rcnn.

Recent approaches for weakly supervised instance segmentations depend on two components: (i) a pseudo label generation model that provides instances which are consistent with a given annotation; and (ii) an instance segmentation model, which is trained in a supervised manner using the pseudo labels as ground-truth. Unlike previous approaches, we explicitly model the uncertainty in the pseudo label generation process using a conditional distribution. The samples drawn from our conditional distribution provide accurate pseudo labels due to the use of semantic class aware unary terms, boundary aware pairwise smoothness terms, and annotation aware higher order terms. Furthermore, we represent the instance segmentation model as an annotation agnostic prediction distribution. In contrast to previous methods, our representation allows us to define a joint probabilistic learning objective that minimizes the dissimilarity between the two distributions. Our approach achieves state of the art results on the PASCAL VOC 2012 data set, outperforming the best baseline by 4.2% [email protected] and 4.8% [email protected].

Semi-supervised learning is attracting blooming attention, due to its success in combining unlabeled data. To mitigate potentially incorrect pseudo labels, recent frameworks mostly set a fixed confidence threshold to discard uncertain samples. This practice ensures high-quality pseudo labels, but incurs a relatively low utilization of the whole unlabeled set. In this work, our key insight is that these uncertain samples can be turned into certain ones, as long as the confusion classes for the top-1 class are detected and removed. Invoked by this, we propose a novel method dubbed ShrinkMatch to learn uncertain samples. For each uncertain sample, it adaptively seeks a shrunk class space, which merely contains the original top-1 class, as well as remaining less likely classes. Since the confusion ones are removed in this space, the re-calculated top-1 confidence can satisfy the pre-defined threshold. We then impose a consistency regularization between a pair of strongly and weakly augmented samples in the shrunk space to strive for discriminative representations. Furthermore, considering the varied reliability among uncertain samples and the gradually improved model during training, we correspondingly design two reweighting principles for our uncertain loss. Our method exhibits impressive performance on widely adopted benchmarks. Code is available at https://github.com/LiheYoung/ShrinkMatch.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

Conditional generative models aim to learn the underlying joint distribution of data and labels to achieve conditional data generation. Among them, the auxiliary classifier generative adversarial network (AC-GAN) has been widely used, but suffers from the problem of low intra-class diversity of the generated samples. The fundamental reason pointed out in this paper is that the classifier of AC-GAN is generator-agnostic, which therefore cannot provide informative guidance for the generator to approach the joint distribution, resulting in a minimization of the conditional entropy that decreases the intra-class diversity. Motivated by this understanding, we propose a novel conditional GAN with an auxiliary discriminative classifier (ADC-GAN) to resolve the above problem. Specifically, the proposed auxiliary discriminative classifier becomes generator-aware by recognizing the class-labels of the real data and the generated data discriminatively. Our theoretical analysis reveals that the generator can faithfully learn the joint distribution even without the original discriminator, making the proposed ADC-GAN robust to the value of the coefficient hyperparameter and the selection of the GAN loss, and stable during training. Extensive experimental results on synthetic and real-world datasets demonstrate the superiority of ADC-GAN in conditional generative modeling compared to state-of-the-art classifier-based and projection-based conditional GANs.

Classifier-Free Guidance (CFG) is a fundamental technique in training conditional diffusion models. The common practice for CFG-based training is to use a single network to learn both conditional and unconditional noise prediction, with a small dropout rate for conditioning. However, we observe that the joint learning of unconditional noise with limited bandwidth in training results in poor priors for the unconditional case. More importantly, these poor unconditional noise predictions become a serious reason for degrading the quality of conditional generation. Inspired by the fact that most CFG-based conditional models are trained by fine-tuning a base model with better unconditional generation, we first show that simply replacing the unconditional noise in CFG with that predicted by the base model can significantly improve conditional generation. Furthermore, we show that a diffusion model other than the one the fine-tuned model was trained on can be used for unconditional noise replacement. We experimentally verify our claim with a range of CFG-based conditional models for both image and video generation, including Zero-1-to-3, Versatile Diffusion, DiT, DynamiCrafter, and InstructPix2Pix.

We introduce a simple but effective unsupervised method for generating realistic and diverse images. We train a class-conditional GAN model without using manually annotated class labels. Instead, our model is conditional on labels automatically derived from clustering in the discriminator's feature space. Our clustering step automatically discovers diverse modes, and explicitly requires the generator to cover them. Experiments on standard mode collapse benchmarks show that our method outperforms several competing methods when addressing mode collapse. Our method also performs well on large-scale datasets such as ImageNet and Places365, improving both image diversity and standard quality metrics, compared to previous methods.

The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We study the use of bootstraps in high-dimensional environments with a small number of resamples. In particular, we show that with a recent "cheap" bootstrap perspective, using a number of resamples as small as one could attain valid coverage even when the dimension grows closely with the sample size, thus strongly supporting the implementability of the bootstrap for large-scale problems. We validate our theoretical results and compare the performance of our approach with other benchmarks via a range of experiments.

Federated Learning (FL) models often experience client drift caused by heterogeneous data, where the distribution of data differs across clients. To address this issue, advanced research primarily focuses on manipulating the existing gradients to achieve more consistent client models. In this paper, we present an alternative perspective on client drift and aim to mitigate it by generating improved local models. First, we analyze the generalization contribution of local training and conclude that this generalization contribution is bounded by the conditional Wasserstein distance between the data distribution of different clients. Then, we propose FedImpro, to construct similar conditional distributions for local training. Specifically, FedImpro decouples the model into high-level and low-level components, and trains the high-level portion on reconstructed feature distributions. This approach enhances the generalization contribution and reduces the dissimilarity of gradients in FL. Experimental results show that FedImpro can help FL defend against data heterogeneity and enhance the generalization performance of the model.

Diffusion models have achieved remarkable success in text-to-image synthesis, largely attributed to the use of classifier-free guidance (CFG), which enables high-quality, condition-aligned image generation. CFG combines the conditional score (e.g., text-conditioned) with the unconditional score to control the output. However, the unconditional score is in charge of estimating the transition between manifolds of adjacent timesteps from x_t to x_{t-1}, which may inadvertently interfere with the trajectory toward the specific condition. In this work, we introduce a novel approach that leverages a geometric perspective on the unconditional score to enhance CFG performance when conditional scores are available. Specifically, we propose a method that filters the singular vectors of both conditional and unconditional scores using singular value decomposition. This filtering process aligns the unconditional score with the conditional score, thereby refining the sampling trajectory to stay closer to the manifold. Our approach improves image quality with negligible additional computation. We provide deeper insights into the score function behavior in diffusion models and present a practical technique for achieving more accurate and contextually coherent image synthesis.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

We address the neural network robustness problem by adding Similarity (i.e., correctly predicted depth-matches into training)-awareness and Distance-to-training-distribution-awareness to the existing output Magnitude (i.e., decision-boundary)-awareness of the softmax function. The resulting SDM activation function provides strong signals of the relative epistemic (reducible) predictive uncertainty. We use this novel behavior to further address the complementary HCI problem of mapping the output to human-interpretable summary statistics over relevant partitions of a held-out calibration set. Estimates of prediction-conditional uncertainty are obtained via a parsimonious learned transform over the class-conditional empirical CDFs of the output of a final-layer SDM activation function. For decision-making and as an intrinsic model check, estimates of class-conditional accuracy are obtained by further partitioning the high-probability regions of this calibrated output into class-conditional, region-specific CDFs. The uncertainty estimates from SDM calibration are remarkably robust to test-time distribution shifts and out-of-distribution inputs; incorporate awareness of the effective sample size; provide estimates of uncertainty from the learning and data splitting processes; and are well-suited for selective classification and conditional branching for additional test-time compute based on the predictive uncertainty, as for selective LLM generation, routing, and composition over multiple models and retrieval. Finally, we construct SDM networks, LLMs with uncertainty-aware verification and interpretability-by-exemplar as intrinsic properties. We provide open-source software implementing these results.

We present a novel generative approach based on Denoising Diffusion Models (DDMs), which produces high-quality image samples along with their losslessly compressed bit-stream representations. This is obtained by replacing the standard Gaussian noise sampling in the reverse diffusion with a selection of noise samples from pre-defined codebooks of fixed iid Gaussian vectors. Surprisingly, we find that our method, termed Denoising Diffusion Codebook Model (DDCM), retains sample quality and diversity of standard DDMs, even for extremely small codebooks. We leverage DDCM and pick the noises from the codebooks that best match a given image, converting our generative model into a highly effective lossy image codec achieving state-of-the-art perceptual image compression results. More generally, by setting other noise selections rules, we extend our compression method to any conditional image generation task (e.g., image restoration), where the generated images are produced jointly with their condensed bit-stream representations. Our work is accompanied by a mathematical interpretation of the proposed compressed conditional generation schemes, establishing a connection with score-based approximations of posterior samplers for the tasks considered.

Recent advancements in generative modeling have made it possible to generate high-quality content from context information, but a key question remains: how to teach models to know when to generate content? To answer this question, this study proposes a novel event generative model that draws its statistical intuition from marked temporal point processes, and offers a clean, flexible, and computationally efficient solution for a wide range of applications involving multi-dimensional marks. We aim to capture the distribution of the point process without explicitly specifying the conditional intensity or probability density. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including exceptional efficiency in learning the model and generating samples, as well as considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

Selecting high-quality data for pre-training is crucial in shaping the downstream task performance of language models. A major challenge lies in identifying this optimal subset, a problem generally considered intractable, thus necessitating scalable and effective heuristics. In this work, we propose a data selection method, CoLoR-Filter (Conditional Loss Reduction Filtering), which leverages an empirical Bayes-inspired approach to derive a simple and computationally efficient selection criterion based on the relative loss values of two auxiliary models. In addition to the modeling rationale, we evaluate CoLoR-Filter empirically on two language modeling tasks: (1) selecting data from C4 for domain adaptation to evaluation on Books and (2) selecting data from C4 for a suite of downstream multiple-choice question answering tasks. We demonstrate favorable scaling both as we subselect more aggressively and using small auxiliary models to select data for large target models. As one headline result, CoLoR-Filter data selected using a pair of 150m parameter auxiliary models can train a 1.2b parameter target model to match a 1.2b parameter model trained on 25b randomly selected tokens with 25x less data for Books and 11x less data for the downstream tasks. Code: https://github.com/davidbrandfonbrener/color-filter-olmo Filtered data: https://huggingface.co/datasets/davidbrandfonbrener/color-filtered-c4

Speech sounds convey a great deal of information about the scenes, resulting in a variety of effects ranging from reverberation to additional ambient sounds. In this paper, we manipulate input speech to sound as though it was recorded within a different scene, given an audio-visual conditional example recorded from that scene. Our model learns through self-supervision, taking advantage of the fact that natural video contains recurring sound events and textures. We extract an audio clip from a video and apply speech enhancement. We then train a latent diffusion model to recover the original speech, using another audio-visual clip taken from elsewhere in the video as a conditional hint. Through this process, the model learns to transfer the conditional example's sound properties to the input speech. We show that our model can be successfully trained using unlabeled, in-the-wild videos, and that an additional visual signal can improve its sound prediction abilities. Please see our project webpage for video results: https://tinglok.netlify.app/files/avsoundscape/

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

The sound effects that designers add to videos are designed to convey a particular artistic effect and, thus, may be quite different from a scene's true sound. Inspired by the challenges of creating a soundtrack for a video that differs from its true sound, but that nonetheless matches the actions occurring on screen, we propose the problem of conditional Foley. We present the following contributions to address this problem. First, we propose a pretext task for training our model to predict sound for an input video clip using a conditional audio-visual clip sampled from another time within the same source video. Second, we propose a model for generating a soundtrack for a silent input video, given a user-supplied example that specifies what the video should "sound like". We show through human studies and automated evaluation metrics that our model successfully generates sound from video, while varying its output according to the content of a supplied example. Project site: https://xypb.github.io/CondFoleyGen/

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning. Our method first trains an unconditional discretization-agnostic denoising model using neural operator architectures. At inference, we refine the samples to satisfy sparse observation data via a gradient-based guidance mechanism. Through rigorous mathematical analysis, we extend Tweedie's formula to infinite-dimensional Hilbert spaces, providing the theoretical foundation for our posterior sampling approach. Our method (FunDPS) accurately captures posterior distributions in function spaces under minimal supervision and severe data scarcity. Across five PDE tasks with only 3% observation, our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines while reducing sampling steps by 4x. Furthermore, multi-resolution fine-tuning ensures strong cross-resolution generalizability. To the best of our knowledge, this is the first diffusion-based framework to operate independently of discretization, offering a practical and flexible solution for forward and inverse problems in the context of PDEs. Code is available at https://github.com/neuraloperator/FunDPS

Structured output representation is a generative task explored in computer vision that often times requires the mapping of low dimensional features to high dimensional structured outputs. Losses in complex spatial information in deterministic approaches such as Convolutional Neural Networks (CNN) lead to uncertainties and ambiguous structures within a single output representation. A probabilistic approach through deep Conditional Generative Models (CGM) is presented by Sohn et al. in which a particular model known as the Conditional Variational Auto-encoder (CVAE) is introduced and explored. While the original paper focuses on the task of image segmentation, this paper adopts the CVAE framework for the task of controlled output representation through attributes. This approach allows us to learn a disentangled multimodal prior distribution, resulting in more controlled and robust approach to sample generation. In this work we recreate the CVAE architecture and train it on images conditioned on various attributes obtained from two image datasets; the Large-scale CelebFaces Attributes (CelebA) dataset and the Caltech-UCSD Birds (CUB-200-2011) dataset. We attempt to generate new faces with distinct attributes such as hair color and glasses, as well as different bird species samples with various attributes. We further introduce strategies for improving generalized sample generation by applying a weighted term to the variational lower bound.

Downsampling layers are crucial building blocks in CNN architectures, which help to increase the receptive field for learning high-level features and reduce the amount of memory/computation in the model. In this work, we study the generalization of the uniform downsampling layer for group equivariant architectures, e.g., G-CNNs. That is, we aim to downsample signals (feature maps) on general finite groups with anti-aliasing. This involves the following: (a) Given a finite group and a downsampling rate, we present an algorithm to form a suitable choice of subgroup. (b) Given a group and a subgroup, we study the notion of bandlimited-ness and propose how to perform anti-aliasing. Notably, our method generalizes the notion of downsampling based on classical sampling theory. When the signal is on a cyclic group, i.e., periodic, our method recovers the standard downsampling of an ideal low-pass filter followed by a subsampling operation. Finally, we conducted experiments on image classification tasks demonstrating that the proposed downsampling operation improves accuracy, better preserves equivariance, and reduces model size when incorporated into G-equivariant networks

Finetuning large language models on instruction data is crucial for enhancing pre-trained knowledge and improving instruction-following capabilities. As instruction datasets proliferate, selecting optimal data for effective training becomes increasingly important. This work addresses the question: How can we determine the optimal subset of data for effective training? While existing research often emphasizes local criteria like instance quality for subset selection, we argue that a global approach focused on data diversity is more critical. Our method employs k-means clustering to ensure the selected subset effectively represents the full dataset. We propose an iterative refinement method inspired by active learning techniques to resample instances from clusters, reassessing each cluster's importance and sampling weight in every training iteration. This approach reduces the effect of outliers and automatically filters out clusters containing low-quality data. Through extensive evaluation across natural language reasoning, general world knowledge, code and math reasoning tasks, and by fine-tuning models from various families, we observe consistent improvements, achieving a 7% increase over random selection and a 3.8% improvement over state-of-the-art sampling methods. Our work highlights the significance of diversity-first sampling when finetuning LLMs to enhance performance across a broad array of evaluation tasks. Our code is available at https://github.com/for-ai/iterative-data-selection.

Despite the proven significance of hyperspectral images (HSIs) in performing various computer vision tasks, its potential is adversely affected by the low-resolution (LR) property in the spatial domain, resulting from multiple physical factors. Inspired by recent advancements in deep generative models, we propose an HSI Super-resolution (SR) approach with Conditional Diffusion Models (HSR-Diff) that merges a high-resolution (HR) multispectral image (MSI) with the corresponding LR-HSI. HSR-Diff generates an HR-HSI via repeated refinement, in which the HR-HSI is initialized with pure Gaussian noise and iteratively refined. At each iteration, the noise is removed with a Conditional Denoising Transformer (CDF ormer) that is trained on denoising at different noise levels, conditioned on the hierarchical feature maps of HR-MSI and LR-HSI. In addition, a progressive learning strategy is employed to exploit the global information of full-resolution images. Systematic experiments have been conducted on four public datasets, demonstrating that HSR-Diff outperforms state-of-the-art methods.

Minibatch optimal transport coupling straightens paths in unconditional flow matching. This leads to computationally less demanding inference as fewer integration steps and less complex numerical solvers can be employed when numerically solving an ordinary differential equation at test time. However, in the conditional setting, minibatch optimal transport falls short. This is because the default optimal transport mapping disregards conditions, resulting in a conditionally skewed prior distribution during training. In contrast, at test time, we have no access to the skewed prior, and instead sample from the full, unbiased prior distribution. This gap between training and testing leads to a subpar performance. To bridge this gap, we propose conditional optimal transport C^2OT that adds a conditional weighting term in the cost matrix when computing the optimal transport assignment. Experiments demonstrate that this simple fix works with both discrete and continuous conditions in 8gaussians-to-moons, CIFAR-10, ImageNet-32x32, and ImageNet-256x256. Our method performs better overall compared to the existing baselines across different function evaluation budgets. Code is available at https://hkchengrex.github.io/C2OT

Sliced-Wasserstein Flow (SWF) is a promising approach to nonparametric generative modeling but has not been widely adopted due to its suboptimal generative quality and lack of conditional modeling capabilities. In this work, we make two major contributions to bridging this gap. First, based on a pleasant observation that (under certain conditions) the SWF of joint distributions coincides with those of conditional distributions, we propose Conditional Sliced-Wasserstein Flow (CSWF), a simple yet effective extension of SWF that enables nonparametric conditional modeling. Second, we introduce appropriate inductive biases of images into SWF with two techniques inspired by local connectivity and multiscale representation in vision research, which greatly improve the efficiency and quality of modeling images. With all the improvements, we achieve generative performance comparable with many deep parametric generative models on both conditional and unconditional tasks in a purely nonparametric fashion, demonstrating its great potential.

Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder varphi^* that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder Phi^*_tau. We prove that non-commutativity steers the optimization towards Phi^*_tau instead of varphi^*, bringing the H-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning Phi^*_tau, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over 2%, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

The emerging conditional coding-based neural video codec (NVC) shows superiority over commonly-used residual coding-based codec and the latest NVC already claims to outperform the best traditional codec. However, there still exist critical problems blocking the practicality of NVC. In this paper, we propose a powerful conditional coding-based NVC that solves two critical problems via feature modulation. The first is how to support a wide quality range in a single model. Previous NVC with this capability only supports about 3.8 dB PSNR range on average. To tackle this limitation, we modulate the latent feature of the current frame via the learnable quantization scaler. During the training, we specially design the uniform quantization parameter sampling mechanism to improve the harmonization of encoding and quantization. This results in a better learning of the quantization scaler and helps our NVC support about 11.4 dB PSNR range. The second is how to make NVC still work under a long prediction chain. We expose that the previous SOTA NVC has an obvious quality degradation problem when using a large intra-period setting. To this end, we propose modulating the temporal feature with a periodically refreshing mechanism to boost the quality. %Besides solving the above two problems, we also design a single model that can support both RGB and YUV colorspaces. Notably, under single intra-frame setting, our codec can achieve 29.7\% bitrate saving over previous SOTA NVC with 16\% MACs reduction. Our codec serves as a notable landmark in the journey of NVC evolution. The codes are at https://github.com/microsoft/DCVC.

We present DySample, an ultra-lightweight and effective dynamic upsampler. While impressive performance gains have been witnessed from recent kernel-based dynamic upsamplers such as CARAFE, FADE, and SAPA, they introduce much workload, mostly due to the time-consuming dynamic convolution and the additional sub-network used to generate dynamic kernels. Further, the need for high-res feature guidance of FADE and SAPA somehow limits their application scenarios. To address these concerns, we bypass dynamic convolution and formulate upsampling from the perspective of point sampling, which is more resource-efficient and can be easily implemented with the standard built-in function in PyTorch. We first showcase a naive design, and then demonstrate how to strengthen its upsampling behavior step by step towards our new upsampler, DySample. Compared with former kernel-based dynamic upsamplers, DySample requires no customized CUDA package and has much fewer parameters, FLOPs, GPU memory, and latency. Besides the light-weight characteristics, DySample outperforms other upsamplers across five dense prediction tasks, including semantic segmentation, object detection, instance segmentation, panoptic segmentation, and monocular depth estimation. Code is available at https://github.com/tiny-smart/dysample.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

Conditional computing processes an input using only part of the neural network's computational units. Learning to execute parts of a deep convolutional network by routing individual samples has several advantages: Reducing the computational burden is an obvious advantage. Furthermore, if similar classes are routed to the same path, that part of the network learns to discriminate between finer differences and better classification accuracies can be attained with fewer parameters. Recently, several papers have exploited this idea to take a particular child of a node in a tree-shaped network or to skip parts of a network. In this work, we follow a Trellis-based approach for generating specific execution paths in a deep convolutional neural network. We have designed routing mechanisms that use differentiable information gain-based cost functions to determine which subset of features in a convolutional layer will be executed. We call our method Conditional Information Gain Trellis (CIGT). We show that our conditional execution mechanism achieves comparable or better model performance compared to unconditional baselines, using only a fraction of the computational resources.

This paper presents Representation-Conditioned image Generation (RCG), a simple yet effective image generation framework which sets a new benchmark in class-unconditional image generation. RCG does not condition on any human annotations. Instead, it conditions on a self-supervised representation distribution which is mapped from the image distribution using a pre-trained encoder. During generation, RCG samples from such representation distribution using a representation diffusion model (RDM), and employs a pixel generator to craft image pixels conditioned on the sampled representation. Such a design provides substantial guidance during the generative process, resulting in high-quality image generation. Tested on ImageNet 256times256, RCG achieves a Frechet Inception Distance (FID) of 3.31 and an Inception Score (IS) of 253.4. These results not only significantly improve the state-of-the-art of class-unconditional image generation but also rival the current leading methods in class-conditional image generation, bridging the long-standing performance gap between these two tasks. Code is available at https://github.com/LTH14/rcg.

Denoising diffusion probabilistic models have been recently proposed to generate high-quality samples by estimating the gradient of the data density. The framework defines the prior noise as a standard Gaussian distribution, whereas the corresponding data distribution may be more complicated than the standard Gaussian distribution, which potentially introduces inefficiency in denoising the prior noise into the data sample because of the discrepancy between the data and the prior. In this paper, we propose PriorGrad to improve the efficiency of the conditional diffusion model for speech synthesis (for example, a vocoder using a mel-spectrogram as the condition) by applying an adaptive prior derived from the data statistics based on the conditional information. We formulate the training and sampling procedures of PriorGrad and demonstrate the advantages of an adaptive prior through a theoretical analysis. Focusing on the speech synthesis domain, we consider the recently proposed diffusion-based speech generative models based on both the spectral and time domains and show that PriorGrad achieves faster convergence and inference with superior performance, leading to an improved perceptual quality and robustness to a smaller network capacity, and thereby demonstrating the efficiency of a data-dependent adaptive prior.

Diffusion probabilistic models (DPMs) have shown remarkable performance in visual synthesis but are computationally expensive due to the need for multiple evaluations during the sampling. Recent predictor-corrector diffusion samplers have significantly reduced the required number of function evaluations (NFE), but inherently suffer from a misalignment issue caused by the extra corrector step, especially with a large classifier-free guidance scale (CFG). In this paper, we introduce a new fast DPM sampler called DC-Solver, which leverages dynamic compensation (DC) to mitigate the misalignment of the predictor-corrector samplers. The dynamic compensation is controlled by compensation ratios that are adaptive to the sampling steps and can be optimized on only 10 datapoints by pushing the sampling trajectory toward a ground truth trajectory. We further propose a cascade polynomial regression (CPR) which can instantly predict the compensation ratios on unseen sampling configurations. Additionally, we find that the proposed dynamic compensation can also serve as a plug-and-play module to boost the performance of predictor-only samplers. Extensive experiments on both unconditional sampling and conditional sampling demonstrate that our DC-Solver can consistently improve the sampling quality over previous methods on different DPMs with a wide range of resolutions up to 1024times1024. Notably, we achieve 10.38 FID (NFE=5) on unconditional FFHQ and 0.394 MSE (NFE=5, CFG=7.5) on Stable-Diffusion-2.1. Code is available at https://github.com/wl-zhao/DC-Solver

Deep generative models are known to produce undesirable samples such as harmful content. Traditional mitigation methods include re-training from scratch, filtering, or editing; however, these are either computationally expensive or can be circumvented by third parties. In this paper, we take a different approach and study how to post-edit an already-trained conditional generative model so that it redacts certain conditionals that will, with high probability, lead to undesirable content. This is done by distilling the conditioning network in the models, giving a solution that is effective, efficient, controllable, and universal for a class of deep generative models. We conduct experiments on redacting prompts in text-to-image models and redacting voices in text-to-speech models. Our method is computationally light, leads to better redaction quality and robustness than baseline methods while still retaining high generation quality.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

In this paper we consider the problem of acoustic inversion in the context of the optoacoustic tomography image reconstruction problem. By leveraging the ability of the recently proposed diffusion models for image generative tasks among others, we devise an image reconstruction architecture based on a conditional diffusion process. The scheme makes use of an initial image reconstruction, which is preprocessed by an autoencoder to generate an adequate representation. This representation is used as conditional information in a generative diffusion process. Although the computational requirements for training and implementing the architecture are not low, several design choices discussed in the work were made to keep them manageable. Numerical results show that the conditional information allows to properly bias the parameters of the diffusion model to improve the quality of the initial reconstructed image, eliminating artifacts or even reconstructing finer details of the ground-truth image that are not recoverable by the initial image reconstruction method. We also tested the proposal under experimental conditions and the obtained results were in line with those corresponding to the numerical simulations. Improvements in image quality up to 17 % in terms of peak signal-to-noise ratio were observed.

We tackle the task of conditional music generation. We introduce MusicGen, a single Language Model (LM) that operates over several streams of compressed discrete music representation, i.e., tokens. Unlike prior work, MusicGen is comprised of a single-stage transformer LM together with efficient token interleaving patterns, which eliminates the need for cascading several models, e.g., hierarchically or upsampling. Following this approach, we demonstrate how MusicGen can generate high-quality samples, while being conditioned on textual description or melodic features, allowing better controls over the generated output. We conduct extensive empirical evaluation, considering both automatic and human studies, showing the proposed approach is superior to the evaluated baselines on a standard text-to-music benchmark. Through ablation studies, we shed light over the importance of each of the components comprising MusicGen. Music samples, code, and models are available at https://github.com/facebookresearch/audiocraft.

When two different parties use the same learning rule on their own data, how can we test whether the distributions of the two outcomes are similar? In this paper, we study the similarity of outcomes of learning rules through the lens of the Total Variation (TV) distance of distributions. We say that a learning rule is TV indistinguishable if the expected TV distance between the posterior distributions of its outputs, executed on two training data sets drawn independently from the same distribution, is small. We first investigate the learnability of hypothesis classes using TV indistinguishable learners. Our main results are information-theoretic equivalences between TV indistinguishability and existing algorithmic stability notions such as replicability and approximate differential privacy. Then, we provide statistical amplification and boosting algorithms for TV indistinguishable learners.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Floods wreak havoc throughout the world, causing billions of dollars in damages, and uprooting communities, ecosystems and economies. The NASA Impact Flood Detection competition tasked participants with predicting flooded pixels after training with synthetic aperture radar (SAR) images in a supervised setting. We propose a semi-supervised learning pseudo-labeling scheme that derives confidence estimates from U-Net ensembles, progressively improving accuracy. Concretely, we use a cyclical approach involving multiple stages (1) training an ensemble model of multiple U-Net architectures with the provided high confidence hand-labeled data and, generated pseudo labels or low confidence labels on the entire unlabeled test dataset, and then, (2) filter out quality generated labels and, (3) combine the generated labels with the previously available high confidence hand-labeled dataset. This assimilated dataset is used for the next round of training ensemble models and the cyclical process is repeated until the performance improvement plateaus. We post process our results with Conditional Random Fields. Our approach sets a new state-of-the-art on the Sentinel-1 dataset with 0.7654 IoU, an impressive improvement over the 0.60 IoU baseline. Our method, which we release with all the code and models, can also be used as an open science benchmark for the Sentinel-1 dataset.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we propose an easily implemented method based on the pivotal sampling algorithm, which we test on problems motivated by learning-based methods for parametric PDEs and uncertainty quantification. In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to 50%. We support our findings with two theoretical results. First, we show that any non-independent leverage score sampling method that obeys a weak one-sided ell_{infty} independence condition (which includes pivotal sampling) can actively learn d dimensional linear functions with O(dlog d) samples, matching independent sampling. This result extends recent work on matrix Chernoff bounds under ell_{infty} independence, and may be of interest for analyzing other sampling strategies beyond pivotal sampling. Second, we show that, for the important case of polynomial regression, our pivotal method obtains an improved bound of O(d) samples.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. Further, we iterate on the two steps again by using the second step's embeddings as new covariates for the next iteration. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples.

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

In this paper, we propose NU-GAN, a new method for resampling audio from lower to higher sampling rates (upsampling). Audio upsampling is an important problem since productionizing generative speech technology requires operating at high sampling rates. Such applications use audio at a resolution of 44.1 kHz or 48 kHz, whereas current speech synthesis methods are equipped to handle a maximum of 24 kHz resolution. NU-GAN takes a leap towards solving audio upsampling as a separate component in the text-to-speech (TTS) pipeline by leveraging techniques for audio generation using GANs. ABX preference tests indicate that our NU-GAN resampler is capable of resampling 22 kHz to 44.1 kHz audio that is distinguishable from original audio only 7.4% higher than random chance for single speaker dataset, and 10.8% higher than chance for multi-speaker dataset.

Music performance synthesis aims to synthesize a musical score into a natural performance. In this paper, we borrow recent advances in text-to-speech synthesis and present the Deep Performer -- a novel system for score-to-audio music performance synthesis. Unlike speech, music often contains polyphony and long notes. Hence, we propose two new techniques for handling polyphonic inputs and providing a fine-grained conditioning in a transformer encoder-decoder model. To train our proposed system, we present a new violin dataset consisting of paired recordings and scores along with estimated alignments between them. We show that our proposed model can synthesize music with clear polyphony and harmonic structures. In a listening test, we achieve competitive quality against the baseline model, a conditional generative audio model, in terms of pitch accuracy, timbre and noise level. Moreover, our proposed model significantly outperforms the baseline on an existing piano dataset in overall quality.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

Classifier-free guidance (CFG) has become the standard method for enhancing the quality of conditional diffusion models. However, employing CFG requires either training an unconditional model alongside the main diffusion model or modifying the training procedure by periodically inserting a null condition. There is also no clear extension of CFG to unconditional models. In this paper, we revisit the core principles of CFG and introduce a new method, independent condition guidance (ICG), which provides the benefits of CFG without the need for any special training procedures. Our approach streamlines the training process of conditional diffusion models and can also be applied during inference on any pre-trained conditional model. Additionally, by leveraging the time-step information encoded in all diffusion networks, we propose an extension of CFG, called time-step guidance (TSG), which can be applied to any diffusion model, including unconditional ones. Our guidance techniques are easy to implement and have the same sampling cost as CFG. Through extensive experiments, we demonstrate that ICG matches the performance of standard CFG across various conditional diffusion models. Moreover, we show that TSG improves generation quality in a manner similar to CFG, without relying on any conditional information.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Deep learning classifiers face significant challenges when dealing with heterogeneous multi-modal and multi-organ biomedical datasets. The low-level feature distinguishability limited to imaging-modality hinders the classifiers' ability to learn high-level semantic relationships, resulting in sub-optimal performance. To address this issue, image augmentation strategies are employed as regularization techniques. While additive noise input during network training is a well-established augmentation as regularization method, modern pipelines often favor more robust techniques such as dropout and weight decay. This preference stems from the observation that combining these established techniques with noise input can adversely affect model performance. In this study, we propose a novel pretraining pipeline that learns to generate conditional noise mask specifically tailored to improve performance on multi-modal and multi-organ datasets. As a reinforcement learning algorithm, our approach employs a dual-component system comprising a very light-weight policy network that learns to sample conditional noise using a differentiable beta distribution as well as a classifier network. The policy network is trained using the reinforce algorithm to generate image-specific noise masks that regularize the classifier during pretraining. A key aspect is that the policy network's role is limited to obtaining an intermediate (or heated) model before fine-tuning. During inference, the policy network is omitted, allowing direct comparison between the baseline and noise-regularized models. We conducted experiments and related analyses on RadImageNet datasets. Results demonstrate that fine-tuning the intermediate models consistently outperforms conventional training algorithms on both classification and generalization to unseen concept tasks.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

This paper contributes to the "BraTS 2024 Brain MR Image Synthesis Challenge" and presents a conditional Wavelet Diffusion Model (cWDM) for directly solving a paired image-to-image translation task on high-resolution volumes. While deep learning-based brain tumor segmentation models have demonstrated clear clinical utility, they typically require MR scans from various modalities (T1, T1ce, T2, FLAIR) as input. However, due to time constraints or imaging artifacts, some of these modalities may be missing, hindering the application of well-performing segmentation algorithms in clinical routine. To address this issue, we propose a method that synthesizes one missing modality image conditioned on three available images, enabling the application of downstream segmentation models. We treat this paired image-to-image translation task as a conditional generation problem and solve it by combining a Wavelet Diffusion Model for high-resolution 3D image synthesis with a simple conditioning strategy. This approach allows us to directly apply our model to full-resolution volumes, avoiding artifacts caused by slice- or patch-wise data processing. While this work focuses on a specific application, the presented method can be applied to all kinds of paired image-to-image translation problems, such as CT leftrightarrow MR and MR leftrightarrow PET translation, or mask-conditioned anatomically guided image generation.

We consider the problem of reconstructing a full 360{\deg} photographic model of an object from a single image of it. We do so by fitting a neural radiance field to the image, but find this problem to be severely ill-posed. We thus take an off-the-self conditional image generator based on diffusion and engineer a prompt that encourages it to "dream up" novel views of the object. Using an approach inspired by DreamFields and DreamFusion, we fuse the given input view, the conditional prior, and other regularizers in a final, consistent reconstruction. We demonstrate state-of-the-art reconstruction results on benchmark images when compared to prior methods for monocular 3D reconstruction of objects. Qualitatively, our reconstructions provide a faithful match of the input view and a plausible extrapolation of its appearance and 3D shape, including to the side of the object not visible in the image.

Conditional generative adversarial networks (cGANs) have shown superior results in class-conditional generation tasks. To simultaneously control multiple conditions, cGANs require multi-label training datasets, where multiple labels can be assigned to each data instance. Nevertheless, the tremendous annotation cost limits the accessibility of multi-label datasets in real-world scenarios. Therefore, in this study we explore the practical setting called the single positive setting, where each data instance is annotated by only one positive label with no explicit negative labels. To generate multi-label data in the single positive setting, we propose a novel sampling approach called single-to-multi-label (S2M) sampling, based on the Markov chain Monte Carlo method. As a widely applicable "add-on" method, our proposed S2M sampling method enables existing unconditional and conditional GANs to draw high-quality multi-label data with a minimal annotation cost. Extensive experiments on real image datasets verify the effectiveness and correctness of our method, even when compared to a model trained with fully annotated datasets.

The objective for establishing dense correspondence between paired images consists of two terms: a data term and a prior term. While conventional techniques focused on defining hand-designed prior terms, which are difficult to formulate, recent approaches have focused on learning the data term with deep neural networks without explicitly modeling the prior, assuming that the model itself has the capacity to learn an optimal prior from a large-scale dataset. The performance improvement was obvious, however, they often fail to address inherent ambiguities of matching, such as textureless regions, repetitive patterns, and large displacements. To address this, we propose DiffMatch, a novel conditional diffusion-based framework designed to explicitly model both the data and prior terms. Unlike previous approaches, this is accomplished by leveraging a conditional denoising diffusion model. DiffMatch consists of two main components: conditional denoising diffusion module and cost injection module. We stabilize the training process and reduce memory usage with a stage-wise training strategy. Furthermore, to boost performance, we introduce an inference technique that finds a better path to the accurate matching field. Our experimental results demonstrate significant performance improvements of our method over existing approaches, and the ablation studies validate our design choices along with the effectiveness of each component. Project page is available at https://ku-cvlab.github.io/DiffMatch/.

Few-shot learning (FSL) has recently been extensively utilized to overcome the scarcity of training data in domain-specific visual recognition. In real-world scenarios, environmental factors such as complex backgrounds, varying lighting conditions, long-distance shooting, and moving targets often cause test images to exhibit numerous incomplete targets or noise disruptions. However, current research on evaluation datasets and methodologies has largely ignored the concept of "environmental robustness", which refers to maintaining consistent performance in complex and diverse physical environments. This neglect has led to a notable decline in the performance of FSL models during practical testing compared to their training performance. To bridge this gap, we introduce a new real-world multi-domain few-shot learning (RD-FSL) benchmark, which includes four domains and six evaluation datasets. The test images in this benchmark feature various challenging elements, such as camouflaged objects, small targets, and blurriness. Our evaluation experiments reveal that existing methods struggle to utilize training images effectively to generate accurate feature representations for challenging test images. To address this problem, we propose a novel conditional representation learning network (CRLNet) that integrates the interactions between training and testing images as conditional information in their respective representation processes. The main goal is to reduce intra-class variance or enhance inter-class variance at the feature representation level. Finally, comparative experiments reveal that CRLNet surpasses the current state-of-the-art methods, achieving performance improvements ranging from 6.83% to 16.98% across diverse settings and backbones. The source code and dataset are available at https://github.com/guoqianyu-alberta/Conditional-Representation-Learning.

Diffusion models have emerged as a pivotal advancement in generative models, setting new standards to the quality of the generated instances. In the current paper we aim to underscore a discrepancy between conventional training methods and the desired conditional sampling behavior of these models. While the prevalent classifier-free guidance technique works well, it's not without flaws. At higher values for the guidance scale parameter w, we often get out of distribution samples and mode collapse, whereas at lower values for w we may not get the desired specificity. To address these challenges, we introduce an updated loss function that better aligns training objectives with sampling behaviors. Experimental validation with FID scores on CIFAR-10 elucidates our method's ability to produce higher quality samples with fewer sampling timesteps, and be more robust to the choice of guidance scale w. We also experiment with fine-tuning Stable Diffusion on the proposed loss, to provide early evidence that large diffusion models may also benefit from this refined loss function.

Beam search is the default decoding strategy for many sequence generation tasks in NLP. The set of approximate K-best items returned by the algorithm is a useful summary of the distribution for many applications; however, the candidates typically exhibit high overlap and may give a highly biased estimate for expectations under our model. These problems can be addressed by instead using stochastic decoding strategies. In this work, we propose a new method for turning beam search into a stochastic process: Conditional Poisson stochastic beam search. Rather than taking the maximizing set at each iteration, we sample K candidates without replacement according to the conditional Poisson sampling design. We view this as a more natural alternative to Kool et. al. 2019's stochastic beam search (SBS). Furthermore, we show how samples generated under the CPSBS design can be used to build consistent estimators and sample diverse sets from sequence models. In our experiments, we observe CPSBS produces lower variance and more efficient estimators than SBS, even showing improvements in high entropy settings.

In this paper, we focus on the task of conditional image generation, where an image is synthesized according to user instructions. The critical challenge underpinning this task is ensuring both the fidelity of the generated images and their semantic alignment with the provided conditions. To tackle this issue, previous studies have employed supervised perceptual losses derived from pre-trained models, i.e., reward models, to enforce alignment between the condition and the generated result. However, we observe one inherent shortcoming: considering the diversity of synthesized images, the reward model usually provides inaccurate feedback when encountering newly generated data, which can undermine the training process. To address this limitation, we propose an uncertainty-aware reward modeling, called Ctrl-U, including uncertainty estimation and uncertainty-aware regularization, designed to reduce the adverse effects of imprecise feedback from the reward model. Given the inherent cognitive uncertainty within reward models, even images generated under identical conditions often result in a relatively large discrepancy in reward loss. Inspired by the observation, we explicitly leverage such prediction variance as an uncertainty indicator. Based on the uncertainty estimation, we regularize the model training by adaptively rectifying the reward. In particular, rewards with lower uncertainty receive higher loss weights, while those with higher uncertainty are given reduced weights to allow for larger variability. The proposed uncertainty regularization facilitates reward fine-tuning through consistency construction. Extensive experiments validate the effectiveness of our methodology in improving the controllability and generation quality, as well as its scalability across diverse conditional scenarios. Code will soon be available at https://grenoble-zhang.github.io/Ctrl-U-Page/.

We explore a generative machine learning-based approach for estimating multi-dimensional probability density functions (PDFs) in a target sample using a statistically independent but related control sample - a common challenge in particle physics data analysis. The generative model must accurately reproduce individual observable distributions while preserving the correlations between them, based on the input multidimensional distribution from the control sample. Here we present a conditional normalizing flow model (CNF) based on a chain of bijectors which learns to transform unpaired simulation events to data events. We assess the performance of the CNF model in the context of LHC Higgs to diphoton analysis, where we use the CNF model to convert a Monte Carlo diphoton sample to one that models data. We show that the CNF model can accurately model complex data distributions and correlations. We also leverage the recently popularized Modified Differential Multiplier Method (MDMM) to improve the convergence of our model and assign physical meaning to usually arbitrary loss-function parameters.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

Existing autoregressive (AR) image generative models use a token-by-token generation schema. That is, they predict a per-token probability distribution and sample the next token from that distribution. The main challenge is how to model the complex distribution of high-dimensional tokens. Previous methods either are too simplistic to fit the distribution or result in slow generation speed. Instead of fitting the distribution of the whole tokens, we explore using a AR model to generate each token in a feature-by-feature way, i.e., taking the generated features as input and generating the next feature. Based on that, we propose ARINAR (AR-in-AR), a bi-level AR model. The outer AR layer take previous tokens as input, predicts a condition vector z for the next token. The inner layer, conditional on z, generates features of the next token autoregressively. In this way, the inner layer only needs to model the distribution of a single feature, for example, using a simple Gaussian Mixture Model. On the ImageNet 256x256 image generation task, ARINAR-B with 213M parameters achieves an FID of 2.75, which is comparable to the state-of-the-art MAR-B model (FID=2.31), while five times faster than the latter.

Autoregressive models are typically applied to sequences of discrete tokens, but recent research indicates that generating sequences of continuous embeddings in an autoregressive manner is also feasible. However, such Continuous Autoregressive Models (CAMs) can suffer from a decline in generation quality over extended sequences due to error accumulation during inference. We introduce a novel method to address this issue by injecting random noise into the input embeddings during training. This procedure makes the model robust against varying error levels at inference. We further reduce error accumulation through an inference procedure that introduces low-level noise. Experiments on musical audio generation show that CAM substantially outperforms existing autoregressive and non-autoregressive approaches while preserving audio quality over extended sequences. This work paves the way for generating continuous embeddings in a purely autoregressive setting, opening new possibilities for real-time and interactive generative applications.

To effectively optimize and personalize treatments, it is necessary to investigate the heterogeneity of treatment effects. With the wide range of users being treated over many online controlled experiments, the typical approach of manually investigating each dimension of heterogeneity becomes overly cumbersome and prone to subjective human biases. We need an efficient way to search through thousands of experiments with hundreds of target covariates and hundreds of breakdown dimensions. In this paper, we propose a systematic paradigm for detecting, surfacing and characterizing heterogeneous treatment effects. First, we detect if treatment effect variation is present in an experiment, prior to specifying any breakdowns. Second, we surface the most relevant dimensions for heterogeneity. Finally, we characterize the heterogeneity beyond just the conditional average treatment effects (CATE) by studying the conditional distributions of the estimated individual treatment effects. We show the effectiveness of our methods using simulated data and empirical studies.

Effective implementations of sampling-based probabilistic inference often require manually constructed, model-specific proposals. Inspired by recent progresses in meta-learning for training learning agents that can generalize to unseen environments, we propose a meta-learning approach to building effective and generalizable MCMC proposals. We parametrize the proposal as a neural network to provide fast approximations to block Gibbs conditionals. The learned neural proposals generalize to occurrences of common structural motifs across different models, allowing for the construction of a library of learned inference primitives that can accelerate inference on unseen models with no model-specific training required. We explore several applications including open-universe Gaussian mixture models, in which our learned proposals outperform a hand-tuned sampler, and a real-world named entity recognition task, in which our sampler yields higher final F1 scores than classical single-site Gibbs sampling.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

We investigate the theoretical foundations of classifier-free guidance (CFG). CFG is the dominant method of conditional sampling for text-to-image diffusion models, yet unlike other aspects of diffusion, it remains on shaky theoretical footing. In this paper, we disprove common misconceptions, by showing that CFG interacts differently with DDPM (Ho et al., 2020) and DDIM (Song et al., 2021), and neither sampler with CFG generates the gamma-powered distribution p(x|c)^gamma p(x)^{1-gamma}. Then, we clarify the behavior of CFG by showing that it is a kind of predictor-corrector method (Song et al., 2020) that alternates between denoising and sharpening, which we call predictor-corrector guidance (PCG). We prove that in the SDE limit, CFG is actually equivalent to combining a DDIM predictor for the conditional distribution together with a Langevin dynamics corrector for a gamma-powered distribution (with a carefully chosen gamma). Our work thus provides a lens to theoretically understand CFG by embedding it in a broader design space of principled sampling methods.

It is widely believed that noise conditioning is indispensable for denoising diffusion models to work successfully. This work challenges this belief. Motivated by research on blind image denoising, we investigate a variety of denoising-based generative models in the absence of noise conditioning. To our surprise, most models exhibit graceful degradation, and in some cases, they even perform better without noise conditioning. We provide a theoretical analysis of the error caused by removing noise conditioning and demonstrate that our analysis aligns with empirical observations. We further introduce a noise-unconditional model that achieves a competitive FID of 2.23 on CIFAR-10, significantly narrowing the gap to leading noise-conditional models. We hope our findings will inspire the community to revisit the foundations and formulations of denoising generative models.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

Datasets scraped from the internet have been critical to the successes of large-scale machine learning. Yet, this very success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision. In this work, we first formalize a system where interactions with one model are recorded as history and scraped as training data in the future. We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions). We find that the degree of bias amplification is closely linked to whether the model's outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration. Experiments in three conditional prediction scenarios - image classification, visual role-labeling, and language generation - demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable. Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems. Code is available at https://github.com/rtaori/data_feedback.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

Denoising diffusion models have emerged as the go-to framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution (OOD) tasks, which remains an under-explored challenge. Realistic reconstructions inconsistent with the measured data can be generated, hallucinating image features that are uniquely present in the training dataset. To simultaneously enforce data-consistency and leverage data-driven priors, we introduce a novel sampling framework called Steerable Conditional Diffusion. This framework adapts the denoising network specifically to the available measured data. Utilising our proposed method, we achieve substantial enhancements in OOD performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.

Diffusion models have made substantial advances in image generation, yet models trained on large, unfiltered datasets often yield outputs misaligned with human preferences. Numerous methods have been proposed to fine-tune pre-trained diffusion models, achieving notable improvements in aligning generated outputs with human preferences. However, we argue that existing preference alignment methods neglect the critical role of handling unconditional/negative-conditional outputs, leading to a diminished capacity to avoid generating undesirable outcomes. This oversight limits the efficacy of classifier-free guidance~(CFG), which relies on the contrast between conditional generation and unconditional/negative-conditional generation to optimize output quality. In response, we propose a straightforward but versatile effective approach that involves training a model specifically attuned to negative preferences. This method does not require new training strategies or datasets but rather involves minor modifications to existing techniques. Our approach integrates seamlessly with models such as SD1.5, SDXL, video diffusion models and models that have undergone preference optimization, consistently enhancing their alignment with human preferences.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for sigma-sub-Gaussian label noise, our analysis provides a regret upper bound of O(sigma^2 d log T) + o(log T), where d is the dimension of the input vector, T is the total number of rounds. We also prove a Omega(sigma^2dlog(T/d)) lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heteroscedastic noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

The field of automatic music composition has seen great progress in recent years, specifically with the invention of transformer-based architectures. When using any deep learning model which considers music as a sequence of events with multiple complex dependencies, the selection of a proper data representation is crucial. In this paper, we tackle the task of conditional drums generation using a novel data encoding scheme inspired by the Compound Word representation, a tokenization process of sequential data. Therefore, we present a sequence-to-sequence architecture where a Bidirectional Long short-term memory (BiLSTM) Encoder receives information about the conditioning parameters (i.e., accompanying tracks and musical attributes), while a Transformer-based Decoder with relative global attention produces the generated drum sequences. We conducted experiments to thoroughly compare the effectiveness of our method to several baselines. Quantitative evaluation shows that our model is able to generate drums sequences that have similar statistical distributions and characteristics to the training corpus. These features include syncopation, compression ratio, and symmetry among others. We also verified, through a listening test, that generated drum sequences sound pleasant, natural and coherent while they "groove" with the given accompaniment.

Diffusion models trained with mean squared error loss tend to generate unrealistic samples. Current state-of-the-art models rely on classifier-free guidance to improve sample quality, yet its surprising effectiveness is not fully understood. In this paper, We show that the effectiveness of classifier-free guidance partly originates from it being a form of implicit perceptual guidance. As a result, we can directly incorporate perceptual loss in diffusion training to improve sample quality. Since the score matching objective used in diffusion training strongly resembles the denoising autoencoder objective used in unsupervised training of perceptual networks, the diffusion model itself is a perceptual network and can be used to generate meaningful perceptual loss. We propose a novel self-perceptual objective that results in diffusion models capable of generating more realistic samples. For conditional generation, our method only improves sample quality without entanglement with the conditional input and therefore does not sacrifice sample diversity. Our method can also improve sample quality for unconditional generation, which was not possible with classifier-free guidance before.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o_p(n^{-1/4}) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models through simulating a set of weighted particles. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and in conditional image generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state of the art.

We present a fast and high-quality codec language model for parallel audio generation. While SoundStorm, a state-of-the-art parallel audio generation model, accelerates inference speed compared to autoregressive models, it still suffers from slow inference due to iterative sampling. To resolve this problem, we propose Group-Masked Language Modeling~(G-MLM) and Group Iterative Parallel Decoding~(G-IPD) for efficient parallel audio generation. Both the training and sampling schemes enable the model to synthesize high-quality audio with a small number of iterations by effectively modeling the group-wise conditional dependencies. In addition, our model employs a cross-attention-based architecture to capture the speaker style of the prompt voice and improves computational efficiency. Experimental results demonstrate that our proposed model outperforms the baselines in prompt-based audio generation.

Denoising Diffusion Probabilistic Models have shown an impressive generation quality, although their long sampling chain leads to high computational costs. In this paper, we observe that a long sampling chain also leads to an error accumulation phenomenon, which is similar to the exposure bias problem in autoregressive text generation. Specifically, we note that there is a discrepancy between training and testing, since the former is conditioned on the ground truth samples, while the latter is conditioned on the previously generated results. To alleviate this problem, we propose a very simple but effective training regularization, consisting in perturbing the ground truth samples to simulate the inference time prediction errors. We empirically show that, without affecting the recall and precision, the proposed input perturbation leads to a significant improvement in the sample quality while reducing both the training and the inference times. For instance, on CelebA 64times64, we achieve a new state-of-the-art FID score of 1.27, while saving 37.5% of the training time. The code is publicly available at https://github.com/forever208/DDPM-IP

The continued release of new and better image generation models increases the demand for synthetic image detectors. In such a dynamic field, detectors need to be able to generalize widely and be robust to uncontrolled alterations. The present work is motivated by this setting, when looking at the role of time, image transformations and data sources, for detector generalization. In these experiments, none of the evaluated detectors is found universal, but results indicate an ensemble could be. Experiments on data collected in the wild show this task to be more challenging than the one defined by large-scale datasets, pointing to a gap between experimentation and actual practice. Finally, we observe a race equilibrium effect, where better generators lead to better detectors, and vice versa. We hypothesize this pushes the field towards a perpetually close race between generators and detectors.

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search benchmarks, we still know little about how they perform in terms of interpolation and extrapolation. In this paper, we demonstrate the importance of separately evaluating the two capabilities of neural retrieval models. Firstly, we examine existing ad-hoc search benchmarks from the two perspectives. We investigate the distribution of training and test data and find a considerable overlap in query entities, query intent, and relevance labels. This finding implies that the evaluation on these test sets is biased toward interpolation and cannot accurately reflect the extrapolation capacity. Secondly, we propose a novel evaluation protocol to separately evaluate the interpolation and extrapolation performance on existing benchmark datasets. It resamples the training and test data based on query similarity and utilizes the resampled dataset for training and evaluation. Finally, we leverage the proposed evaluation protocol to comprehensively revisit a number of widely-adopted neural retrieval models. Results show models perform differently when moving from interpolation to extrapolation. For example, representation-based retrieval models perform almost as well as interaction-based retrieval models in terms of interpolation but not extrapolation. Therefore, it is necessary to separately evaluate both interpolation and extrapolation performance and the proposed resampling method serves as a simple yet effective evaluation tool for future IR studies.

We tackle the problem of generating audio samples conditioned on descriptive text captions. In this work, we propose AaudioGen, an auto-regressive generative model that generates audio samples conditioned on text inputs. AudioGen operates on a learnt discrete audio representation. The task of text-to-audio generation poses multiple challenges. Due to the way audio travels through a medium, differentiating ``objects'' can be a difficult task (e.g., separating multiple people simultaneously speaking). This is further complicated by real-world recording conditions (e.g., background noise, reverberation, etc.). Scarce text annotations impose another constraint, limiting the ability to scale models. Finally, modeling high-fidelity audio requires encoding audio at high sampling rate, leading to extremely long sequences. To alleviate the aforementioned challenges we propose an augmentation technique that mixes different audio samples, driving the model to internally learn to separate multiple sources. We curated 10 datasets containing different types of audio and text annotations to handle the scarcity of text-audio data points. For faster inference, we explore the use of multi-stream modeling, allowing the use of shorter sequences while maintaining a similar bitrate and perceptual quality. We apply classifier-free guidance to improve adherence to text. Comparing to the evaluated baselines, AudioGen outperforms over both objective and subjective metrics. Finally, we explore the ability of the proposed method to generate audio continuation conditionally and unconditionally. Samples: https://felixkreuk.github.io/audiogen

In semi-supervised learning, unlabeled samples can be utilized through augmentation and consistency regularization. However, we observed certain samples, even undergoing strong augmentation, are still correctly classified with high confidence, resulting in a loss close to zero. It indicates that these samples have been already learned well and do not provide any additional optimization benefits to the model. We refer to these samples as ``naive samples". Unfortunately, existing SSL models overlook the characteristics of naive samples, and they just apply the same learning strategy to all samples. To further optimize the SSL model, we emphasize the importance of giving attention to naive samples and augmenting them in a more diverse manner. Sample adaptive augmentation (SAA) is proposed for this stated purpose and consists of two modules: 1) sample selection module; 2) sample augmentation module. Specifically, the sample selection module picks out {naive samples} based on historical training information at each epoch, then the naive samples will be augmented in a more diverse manner in the sample augmentation module. Thanks to the extreme ease of implementation of the above modules, SAA is advantageous for being simple and lightweight. We add SAA on top of FixMatch and FlexMatch respectively, and experiments demonstrate SAA can significantly improve the models. For example, SAA helped improve the accuracy of FixMatch from 92.50% to 94.76% and that of FlexMatch from 95.01% to 95.31% on CIFAR-10 with 40 labels.

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability eta(x)=P(Y=1mid X=x), we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of 2eta(x)-1 and apply the method to real datasets.

Distributional shift is a central challenge in the deployment of machine learning models as they can be ill-equipped for real-world data. This is particularly evident in text-to-audio generation where the encoded representations are easily undermined by unseen prompts, which leads to the degradation of generated audio -- the limited set of the text-audio pairs remains inadequate for conditional audio generation in the wild as user prompts are under-specified. In particular, we observe a consistent audio quality degradation in generated audio samples with user prompts, as opposed to training set prompts. To this end, we present a retrieval-based in-context prompt editing framework that leverages the training captions as demonstrative exemplars to revisit the user prompts. We show that the framework enhanced the audio quality across the set of collected user prompts, which were edited with reference to the training captions as exemplars.

We propose a new method for generating realistic datasets with distribution shifts using any decoder-based generative model. Our approach systematically creates datasets with varying intensities of distribution shifts, facilitating a comprehensive analysis of model performance degradation. We then use these generated datasets to evaluate the performance of various commonly used networks and observe a consistent decline in performance with increasing shift intensity, even when the effect is almost perceptually unnoticeable to the human eye. We see this degradation even when using data augmentations. We also find that enlarging the training dataset beyond a certain point has no effect on the robustness and that stronger inductive biases increase robustness.

This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the sensor made an incomplete observation. This leads to a bias toward lower values in labels and the resultant learning because labels may have lower values due to incomplete observations, even if the actual magnitude of the phenomenon was high. Moreover, because an incomplete observation does not provide any tags indicating incompleteness, we cannot eliminate or impute them. To address this issue, we propose a learning algorithm that explicitly models incomplete observations corrupted with an asymmetric noise that always has a negative value. We show that our algorithm is unbiased as if it were learned from uncorrupted data that does not involve incomplete observations. We demonstrate the advantages of our algorithm through numerical experiments.

Current diffusion-based image restoration methods feed degraded input images as conditions into the noise estimation network. However, interpreting this diffusion process is challenging since it essentially generates the target image from the noise. To establish a unified and more interpretable model for image generation and restoration, we propose residual denoising diffusion models (RDDM). In contrast to existing diffusion models (e.g., DDPM or DDIM) that focus solely on noise estimation, our RDDM predicts residuals to represent directional diffusion from the target domain to the input domain, while concurrently estimating noise to account for random perturbations in the diffusion process. The introduction of residuals allows us to redefine the forward diffusion process, wherein the target image progressively diffuses into a purely noisy image or a noise-carrying input image, thus unifying image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation, and propose a partially path-independent generation process to better understand the reverse process. Notably, with native support for conditional inputs, our RDDM enables a generic UNet, trained with only an ell _1 loss and a batch size of 1, to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration, application, and development of our innovative framework (https://github.com/nachifur/RDDM).

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.

Large pre-trained models for zero/few-shot learning excel in language and vision domains but encounter challenges in multivariate time series (TS) due to the diverse nature and scarcity of publicly available pre-training data. Consequently, there has been a recent surge in utilizing pre-trained large language models (LLMs) with token adaptations for TS forecasting. These approaches employ cross-domain transfer learning and surprisingly yield impressive results. However, these models are typically very slow and large (~billion parameters) and do not consider cross-channel correlations. To address this, we present Tiny Time Mixers (TTM), a significantly small model based on the lightweight TSMixer architecture. TTM marks the first success in developing fast and tiny general pre-trained models (<1M parameters), exclusively trained on public TS datasets, with effective transfer learning capabilities for forecasting. To tackle the complexity of pre-training on multiple datasets with varied temporal resolutions, we introduce several novel enhancements such as adaptive patching, dataset augmentation via downsampling, and resolution prefix tuning. Moreover, we employ a multi-level modeling strategy to effectively model channel correlations and infuse exogenous signals during fine-tuning, a crucial capability lacking in existing benchmarks. TTM shows significant accuracy gains (12-38\%) over popular benchmarks in few/zero-shot forecasting. It also drastically reduces the compute needs as compared to LLM-TS methods, with a 14X cut in learnable parameters, 106X less total parameters, and substantial reductions in fine-tuning (65X) and inference time (54X). In fact, TTM's zero-shot often surpasses the few-shot results in many popular benchmarks, highlighting the efficacy of our approach. Code and pre-trained models will be open-sourced.

We propose a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress all the time steps with the gradient backpropagated from the score network. In order to produce meaningful gradients for the generator, the score network is trained to simultaneously match the real data distribution and mismatch the fake data distribution. This model has the following advantages: 1) For sampling, it generates a fake image with only one step forward. 2) For training, it only needs 10 diffusion steps.3) Compared with consistency model, it is free of the ill-posed problem caused by consistency loss. On the popular CIFAR-10 dataset, our model outperforms Consistency Model and Denoising Score Matching, which demonstrates the potential of the framework. We further provide more examples on the MINIST and LSUN datasets. The code is available on GitHub.

The capability of video super-resolution (VSR) to synthesize high-resolution (HR) video from ideal datasets has been demonstrated in many works. However, applying the VSR model to real-world video with unknown and complex degradation remains a challenging task. First, existing degradation metrics in most VSR methods are not able to effectively simulate real-world noise and blur. On the contrary, simple combinations of classical degradation are used for real-world noise modeling, which led to the VSR model often being violated by out-of-distribution noise. Second, many SR models focus on noise simulation and transfer. Nevertheless, the sampled noise is monotonous and limited. To address the aforementioned problems, we propose a Negatives augmentation strategy for generalized noise modeling in Video Super-Resolution (NegVSR) task. Specifically, we first propose sequential noise generation toward real-world data to extract practical noise sequences. Then, the degeneration domain is widely expanded by negative augmentation to build up various yet challenging real-world noise sets. We further propose the augmented negative guidance loss to learn robust features among augmented negatives effectively. Extensive experiments on real-world datasets (e.g., VideoLQ and FLIR) show that our method outperforms state-of-the-art methods with clear margins, especially in visual quality.

Data augmentation is a crucial component in unsupervised contrastive learning (CL). It determines how positive samples are defined and, ultimately, the quality of the learned representation. In this work, we open the door to new perspectives for CL by integrating prior knowledge, given either by generative models -- viewed as prior representations -- or weak attributes in the positive and negative sampling. To this end, we use kernel theory to propose a novel loss, called decoupled uniformity, that i) allows the integration of prior knowledge and ii) removes the negative-positive coupling in the original InfoNCE loss. We draw a connection between contrastive learning and conditional mean embedding theory to derive tight bounds on the downstream classification loss. In an unsupervised setting, we empirically demonstrate that CL benefits from generative models to improve its representation both on natural and medical images. In a weakly supervised scenario, our framework outperforms other unconditional and conditional CL approaches.

Classifier-free guidance (CFG) is crucial for improving both generation quality and alignment between the input condition and final output in diffusion models. While a high guidance scale is generally required to enhance these aspects, it also causes oversaturation and unrealistic artifacts. In this paper, we revisit the CFG update rule and introduce modifications to address this issue. We first decompose the update term in CFG into parallel and orthogonal components with respect to the conditional model prediction and observe that the parallel component primarily causes oversaturation, while the orthogonal component enhances image quality. Accordingly, we propose down-weighting the parallel component to achieve high-quality generations without oversaturation. Additionally, we draw a connection between CFG and gradient ascent and introduce a new rescaling and momentum method for the CFG update rule based on this insight. Our approach, termed adaptive projected guidance (APG), retains the quality-boosting advantages of CFG while enabling the use of higher guidance scales without oversaturation. APG is easy to implement and introduces practically no additional computational overhead to the sampling process. Through extensive experiments, we demonstrate that APG is compatible with various conditional diffusion models and samplers, leading to improved FID, recall, and saturation scores while maintaining precision comparable to CFG, making our method a superior plug-and-play alternative to standard classifier-free guidance.

There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C, even if C is included in its training set. Roughly speaking, a generative model p is $k-NAF if for every potentially copyrighted data C, the output of p diverges by at most k-bits from the output of a model q that did not access C at all$. We also give generative model learning algorithms, which efficiently modify the original generative model learning algorithm in a black box manner, that output generative models with strong bounds on the probability of sampling protected content. Furthermore, we provide promising experiments for both language (transformers) and image (diffusion) generative models, showing minimal degradation in output quality while ensuring strong protections against sampling protected content.

We explore the use of Residual Vector Quantization (RVQ) for high-fidelity generation in vector-quantized generative models. This quantization technique maintains higher data fidelity by employing more in-depth tokens. However, increasing the token number in generative models leads to slower inference speeds. To this end, we introduce ResGen, an efficient RVQ-based discrete diffusion model that generates high-fidelity samples without compromising sampling speed. Our key idea is a direct prediction of vector embedding of collective tokens rather than individual ones. Moreover, we demonstrate that our proposed token masking and multi-token prediction method can be formulated within a principled probabilistic framework using a discrete diffusion process and variational inference. We validate the efficacy and generalizability of the proposed method on two challenging tasks across different modalities: conditional image generation} on ImageNet 256x256 and zero-shot text-to-speech synthesis. Experimental results demonstrate that ResGen outperforms autoregressive counterparts in both tasks, delivering superior performance without compromising sampling speed. Furthermore, as we scale the depth of RVQ, our generative models exhibit enhanced generation fidelity or faster sampling speeds compared to similarly sized baseline models. The project page can be found at https://resgen-genai.github.io

Recently, convolutional networks have achieved remarkable development in remote sensing image Super-Resoltuion (SR) by minimizing the regression objectives, e.g., MSE loss. However, despite achieving impressive performance, these methods often suffer from poor visual quality with over-smooth issues. Generative adversarial networks have the potential to infer intricate details, but they are easy to collapse, resulting in undesirable artifacts. To mitigate these issues, in this paper, we first introduce Diffusion Probabilistic Model (DPM) for efficient remote sensing image SR, dubbed EDiffSR. EDiffSR is easy to train and maintains the merits of DPM in generating perceptual-pleasant images. Specifically, different from previous works using heavy UNet for noise prediction, we develop an Efficient Activation Network (EANet) to achieve favorable noise prediction performance by simplified channel attention and simple gate operation, which dramatically reduces the computational budget. Moreover, to introduce more valuable prior knowledge into the proposed EDiffSR, a practical Conditional Prior Enhancement Module (CPEM) is developed to help extract an enriched condition. Unlike most DPM-based SR models that directly generate conditions by amplifying LR images, the proposed CPEM helps to retain more informative cues for accurate SR. Extensive experiments on four remote sensing datasets demonstrate that EDiffSR can restore visual-pleasant images on simulated and real-world remote sensing images, both quantitatively and qualitatively. The code of EDiffSR will be available at https://github.com/XY-boy/EDiffSR

Conditional visual generation has witnessed remarkable progress with the advent of diffusion models (DMs), especially in tasks like control-to-image generation. However, challenges such as expensive computational cost, high inference latency, and difficulties of integration with large language models (LLMs) have necessitated exploring alternatives to DMs. This paper introduces ControlVAR, a novel framework that explores pixel-level controls in visual autoregressive (VAR) modeling for flexible and efficient conditional generation. In contrast to traditional conditional models that learn the conditional distribution, ControlVAR jointly models the distribution of image and pixel-level conditions during training and imposes conditional controls during testing. To enhance the joint modeling, we adopt the next-scale AR prediction paradigm and unify control and image representations. A teacher-forcing guidance strategy is proposed to further facilitate controllable generation with joint modeling. Extensive experiments demonstrate the superior efficacy and flexibility of ControlVAR across various conditional generation tasks against popular conditional DMs, \eg, ControlNet and T2I-Adaptor. Code: https://github.com/lxa9867/ControlVAR.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Classifier-free guidance has become a staple for conditional generation with denoising diffusion models. However, a comprehensive understanding of classifier-free guidance is still missing. In this work, we carry out an empirical study to provide a fresh perspective on classifier-free guidance. Concretely, instead of solely focusing on classifier-free guidance, we trace back to the root, i.e., classifier guidance, pinpoint the key assumption for the derivation, and conduct a systematic study to understand the role of the classifier. We find that both classifier guidance and classifier-free guidance achieve conditional generation by pushing the denoising diffusion trajectories away from decision boundaries, i.e., areas where conditional information is usually entangled and is hard to learn. Based on this classifier-centric understanding, we propose a generic postprocessing step built upon flow-matching to shrink the gap between the learned distribution for a pre-trained denoising diffusion model and the real data distribution, majorly around the decision boundaries. Experiments on various datasets verify the effectiveness of the proposed approach.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

Conditional diffusion models have shown remarkable performance in various generative tasks, but training them requires large-scale datasets that often contain noise in conditional inputs, a.k.a. noisy labels. This noise leads to condition mismatch and quality degradation of generated data. This paper proposes Transition-aware weighted Denoising Score Matching (TDSM) for training conditional diffusion models with noisy labels, which is the first study in the line of diffusion models. The TDSM objective contains a weighted sum of score networks, incorporating instance-wise and time-dependent label transition probabilities. We introduce a transition-aware weight estimator, which leverages a time-dependent noisy-label classifier distinctively customized to the diffusion process. Through experiments across various datasets and noisy label settings, TDSM improves the quality of generated samples aligned with given conditions. Furthermore, our method improves generation performance even on prevalent benchmark datasets, which implies the potential noisy labels and their risk of generative model learning. Finally, we show the improved performance of TDSM on top of conventional noisy label corrections, which empirically proving its contribution as a part of label-noise robust generative models. Our code is available at: https://github.com/byeonghu-na/tdsm.

Data scarcity in the brain-computer interface field can be alleviated through the use of generative models, specifically diffusion models. While diffusion models have previously been successfully applied to electroencephalogram (EEG) data, existing models lack flexibility w.r.t.~sampling or require alternative representations of the EEG data. To overcome these limitations, we introduce a novel approach to conditional diffusion models that utilizes classifier-free guidance to directly generate subject-, session-, and class-specific EEG data. In addition to commonly used metrics, domain-specific metrics are employed to evaluate the specificity of the generated samples. The results indicate that the proposed model can generate EEG data that resembles real data for each subject, session, and class.

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e., the problem of learning with noisy labels on long-tailed data. Previous works develop several methods for the problem. However, they always rely on strong assumptions that are invalid or hard to be checked in practice. In this paper, to handle the problem and address the limitations of prior works, we propose a representation calibration method RCAL. Specifically, RCAL works with the representations extracted by unsupervised contrastive learning. We assume that without incorrect labeling and class imbalance, the representations of instances in each class conform to a multivariate Gaussian distribution, which is much milder and easier to be checked. Based on the assumption, we recover underlying representation distributions from polluted ones resulting from mislabeled and class-imbalanced data. Additional data points are then sampled from the recovered distributions to help generalization. Moreover, during classifier training, representation learning takes advantage of representation robustness brought by contrastive learning, which further improves the classifier performance. We derive theoretical results to discuss the effectiveness of our representation calibration. Experiments on multiple benchmarks justify our claims and confirm the superiority of the proposed method.

In this paper, we propose LSRNA, a novel framework for higher-resolution (exceeding 1K) image generation using diffusion models by leveraging super-resolution directly in the latent space. Existing diffusion models struggle with scaling beyond their training resolutions, often leading to structural distortions or content repetition. Reference-based methods address the issues by upsampling a low-resolution reference to guide higher-resolution generation. However, they face significant challenges: upsampling in latent space often causes manifold deviation, which degrades output quality. On the other hand, upsampling in RGB space tends to produce overly smoothed outputs. To overcome these limitations, LSRNA combines Latent space Super-Resolution (LSR) for manifold alignment and Region-wise Noise Addition (RNA) to enhance high-frequency details. Our extensive experiments demonstrate that integrating LSRNA outperforms state-of-the-art reference-based methods across various resolutions and metrics, while showing the critical role of latent space upsampling in preserving detail and sharpness. The code is available at https://github.com/3587jjh/LSRNA.

A major challenge in structured prediction is to represent the interdependencies within output structures. When outputs are structured as sequences, linear-chain conditional random fields (CRFs) are a widely used model class which can learn local dependencies in the output. However, the CRF's Markov assumption makes it impossible for CRFs to represent distributions with nonlocal dependencies, and standard CRFs are unable to respect nonlocal constraints of the data (such as global arity constraints on output labels). We present a generalization of CRFs that can enforce a broad class of constraints, including nonlocal ones, by specifying the space of possible output structures as a regular language L. The resulting regular-constrained CRF (RegCCRF) has the same formal properties as a standard CRF, but assigns zero probability to all label sequences not in L. Notably, RegCCRFs can incorporate their constraints during training, while related models only enforce constraints during decoding. We prove that constrained training is never worse than constrained decoding, and show empirically that it can be substantially better in practice. Additionally, we demonstrate a practical benefit on downstream tasks by incorporating a RegCCRF into a deep neural model for semantic role labeling, exceeding state-of-the-art results on a standard dataset.

Supervised learning usually requires a large amount of labelled data. However, attaining ground-truth labels is costly for many tasks. Alternatively, weakly supervised methods learn with cheap weak signals that only approximately label some data. Many existing weakly supervised learning methods learn a deterministic function that estimates labels given the input data and weak signals. In this paper, we develop label learning flows (LLF), a general framework for weakly supervised learning problems. Our method is a generative model based on normalizing flows. The main idea of LLF is to optimize the conditional likelihoods of all possible labelings of the data within a constrained space defined by weak signals. We develop a training method for LLF that trains the conditional flow inversely and avoids estimating the labels. Once a model is trained, we can make predictions with a sampling algorithm. We apply LLF to three weakly supervised learning problems. Experiment results show that our method outperforms many baselines we compare against.

In this work, we introduce ChemBFN, a language model that handles chemistry tasks based on Bayesian flow networks working on discrete data. A new accuracy schedule is proposed to improve the sampling quality by significantly reducing the reconstruction loss. We show evidence that our method is appropriate for generating molecules with satisfied diversity even when a smaller number of sampling steps is used. A classifier-free guidance method is adapted for conditional generation. It is also worthwhile to point out that after generative training, our model can be fine-tuned on regression and classification tasks with the state-of-the-art performance, which opens the gate of building all-in-one models in a single module style. Our model has been open sourced at https://github.com/Augus1999/bayesian-flow-network-for-chemistry.

We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior knowledge of the unknown signal is helpful for accurate recovery. Motivated by the power of score-based generative models (SGM, also known as diffusion models) in capturing the rich structure of natural signals beyond simple sparsity, we propose an unsupervised data-driven approach called quantized compressed sensing with SGM (QCS-SGM), where the prior distribution is modeled by a pre-trained SGM. To perform posterior sampling, an annealed pseudo-likelihood score called noise perturbed pseudo-likelihood score is introduced and combined with the prior score of SGM. The proposed QCS-SGM applies to an arbitrary number of quantization bits. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM significantly outperforms existing state-of-the-art algorithms by a large margin for both in-distribution and out-of-distribution samples. Moreover, as a posterior sampling method, QCS-SGM can be easily used to obtain confidence intervals or uncertainty estimates of the reconstructed results. The code is available at https://github.com/mengxiangming/QCS-SGM.

Previous works (Donahue et al., 2018a; Engel et al., 2019a) have found that generating coherent raw audio waveforms with GANs is challenging. In this paper, we show that it is possible to train GANs reliably to generate high quality coherent waveforms by introducing a set of architectural changes and simple training techniques. Subjective evaluation metric (Mean Opinion Score, or MOS) shows the effectiveness of the proposed approach for high quality mel-spectrogram inversion. To establish the generality of the proposed techniques, we show qualitative results of our model in speech synthesis, music domain translation and unconditional music synthesis. We evaluate the various components of the model through ablation studies and suggest a set of guidelines to design general purpose discriminators and generators for conditional sequence synthesis tasks. Our model is non-autoregressive, fully convolutional, with significantly fewer parameters than competing models and generalizes to unseen speakers for mel-spectrogram inversion. Our pytorch implementation runs at more than 100x faster than realtime on GTX 1080Ti GPU and more than 2x faster than real-time on CPU, without any hardware specific optimization tricks.

Denoising diffusion probabilistic models (DDPMs) have been proven capable of synthesizing high-quality images with remarkable diversity when trained on large amounts of data. Typical diffusion models and modern large-scale conditional generative models like text-to-image generative models are vulnerable to overfitting when fine-tuned on extremely limited data. Existing works have explored subject-driven generation using a reference set containing a few images. However, few prior works explore DDPM-based domain-driven generation, which aims to learn the common features of target domains while maintaining diversity. This paper proposes a novel DomainStudio approach to adapt DDPMs pre-trained on large-scale source datasets to target domains using limited data. It is designed to keep the diversity of subjects provided by source domains and get high-quality and diverse adapted samples in target domains. We propose to keep the relative distances between adapted samples to achieve considerable generation diversity. In addition, we further enhance the learning of high-frequency details for better generation quality. Our approach is compatible with both unconditional and conditional diffusion models. This work makes the first attempt to realize unconditional few-shot image generation with diffusion models, achieving better quality and greater diversity than current state-of-the-art GAN-based approaches. Moreover, this work also significantly relieves overfitting for conditional generation and realizes high-quality domain-driven generation, further expanding the applicable scenarios of modern large-scale text-to-image models.

Lately, post-training quantization methods have gained considerable attention, as they are simple to use, and require only a small unlabeled calibration set. This small dataset cannot be used to fine-tune the model without significant over-fitting. Instead, these methods only use the calibration set to set the activations' dynamic ranges. However, such methods always resulted in significant accuracy degradation, when used below 8-bits (except on small datasets). Here we aim to break the 8-bit barrier. To this end, we minimize the quantization errors of each layer separately by optimizing its parameters over the calibration set. We empirically demonstrate that this approach is: (1) much less susceptible to over-fitting than the standard fine-tuning approaches, and can be used even on a very small calibration set; and (2) more powerful than previous methods, which only set the activations' dynamic ranges. Furthermore, we demonstrate how to optimally allocate the bit-widths for each layer, while constraining accuracy degradation or model compression by proposing a novel integer programming formulation. Finally, we suggest model global statistics tuning, to correct biases introduced during quantization. Together, these methods yield state-of-the-art results for both vision and text models. For instance, on ResNet50, we obtain less than 1\% accuracy degradation --- with 4-bit weights and activations in all layers, but the smallest two. We open-sourced our code.

Diffusion models have demonstrated superior performance across various generative tasks including images, videos, and audio. However, they encounter difficulties in directly generating high-resolution samples. Previously proposed solutions to this issue involve modifying the architecture, further training, or partitioning the sampling process into multiple stages. These methods have the limitation of not being able to directly utilize pre-trained models as-is, requiring additional work. In this paper, we introduce upsample guidance, a technique that adapts pretrained diffusion model (e.g., 512^2) to generate higher-resolution images (e.g., 1536^2) by adding only a single term in the sampling process. Remarkably, this technique does not necessitate any additional training or relying on external models. We demonstrate that upsample guidance can be applied to various models, such as pixel-space, latent space, and video diffusion models. We also observed that the proper selection of guidance scale can improve image quality, fidelity, and prompt alignment.

Minority samples are underrepresented instances located in low-density regions of a data manifold, and are valuable in many generative AI applications, such as data augmentation, creative content generation, etc. Unfortunately, existing diffusion-based minority generators often rely on computationally expensive guidance dedicated for minority generation. To address this, here we present a simple yet powerful guidance-free approach called Boost-and-Skip for generating minority samples using diffusion models. The key advantage of our framework requires only two minimal changes to standard generative processes: (i) variance-boosted initialization and (ii) timestep skipping. We highlight that these seemingly-trivial modifications are supported by solid theoretical and empirical evidence, thereby effectively promoting emergence of underrepresented minority features. Our comprehensive experiments demonstrate that Boost-and-Skip greatly enhances the capability of generating minority samples, even rivaling guidance-based state-of-the-art approaches while requiring significantly fewer computations. Code is available at https://github.com/soobin-um/BnS.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

We investigate the use of a stratified sampling approach for LIME Image, a popular model-agnostic explainable AI method for computer vision tasks, in order to reduce the artifacts generated by typical Monte Carlo sampling. Such artifacts are due to the undersampling of the dependent variable in the synthetic neighborhood around the image being explained, which may result in inadequate explanations due to the impossibility of fitting a linear regressor on the sampled data. We then highlight a connection with the Shapley theory, where similar arguments about undersampling and sample relevance were suggested in the past. We derive all the formulas and adjustment factors required for an unbiased stratified sampling estimator. Experiments show the efficacy of the proposed approach.

Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and noisy images. Some approaches leverage such unpaired data to train denoisers in a supervised manner by generating synthetic clean-noisy pairs. However, these methods often fall short due to the distribution gap between synthetic and real noisy images. To mitigate this issue, we propose a solution based on input sparsification, specifically using random input masking. Our method, which we refer to as Mask, Inpaint and Denoise (MID), trains a denoiser to simultaneously denoise and inpaint synthetic clean-noisy pairs. On one hand, input sparsification reduces the gap between synthetic and real noisy images. On the other hand, an inpainter trained in a supervised manner can still accurately reconstruct sparse inputs by predicting missing clean pixels using the remaining unmasked pixels. Our approach begins with a synthetic Gaussian noise sampler and iteratively refines it using a noise dataset derived from the denoiser's predictions. The noise dataset is created by subtracting predicted pseudo-clean images from real noisy images at each iteration. The core intuition is that improving the denoiser results in a more accurate noise dataset and, consequently, a better noise sampler. We validate our method through extensive experiments on real-world noisy image datasets, demonstrating competitive performance compared to existing unsupervised denoising methods.

Text-to-image diffusion models have achieved tremendous success in the field of controllable image generation, while also coming along with issues of privacy leakage and data copyrights. Membership inference arises in these contexts as a potential auditing method for detecting unauthorized data usage. While some efforts have been made on diffusion models, they are not applicable to text-to-image diffusion models due to the high computation overhead and enhanced generalization capabilities. In this paper, we first identify a conditional overfitting phenomenon in text-to-image diffusion models, indicating that these models tend to overfit the conditional distribution of images given the corresponding text rather than the marginal distribution of images only. Based on this observation, we derive an analytical indicator, namely Conditional Likelihood Discrepancy (CLiD), to perform membership inference, which reduces the stochasticity in estimating memorization of individual samples. Experimental results demonstrate that our method significantly outperforms previous methods across various data distributions and dataset scales. Additionally, our method shows superior resistance to overfitting mitigation strategies, such as early stopping and data augmentation.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

We consider the problem of generating musical soundtracks in sync with rhythmic visual cues. Most existing works rely on pre-defined music representations, leading to the incompetence of generative flexibility and complexity. Other methods directly generating video-conditioned waveforms suffer from limited scenarios, short lengths, and unstable generation quality. To this end, we present Long-Term Rhythmic Video Soundtracker (LORIS), a novel framework to synthesize long-term conditional waveforms. Specifically, our framework consists of a latent conditional diffusion probabilistic model to perform waveform synthesis. Furthermore, a series of context-aware conditioning encoders are proposed to take temporal information into consideration for a long-term generation. Notably, we extend our model's applicability from dances to multiple sports scenarios such as floor exercise and figure skating. To perform comprehensive evaluations, we establish a benchmark for rhythmic video soundtracks including the pre-processed dataset, improved evaluation metrics, and robust generative baselines. Extensive experiments show that our model generates long-term soundtracks with state-of-the-art musical quality and rhythmic correspondence. Codes are available at https://github.com/OpenGVLab/LORIS.

In this paper, we show that a binary latent space can be explored for compact yet expressive image representations. We model the bi-directional mappings between an image and the corresponding latent binary representation by training an auto-encoder with a Bernoulli encoding distribution. On the one hand, the binary latent space provides a compact discrete image representation of which the distribution can be modeled more efficiently than pixels or continuous latent representations. On the other hand, we now represent each image patch as a binary vector instead of an index of a learned cookbook as in discrete image representations with vector quantization. In this way, we obtain binary latent representations that allow for better image quality and high-resolution image representations without any multi-stage hierarchy in the latent space. In this binary latent space, images can now be generated effectively using a binary latent diffusion model tailored specifically for modeling the prior over the binary image representations. We present both conditional and unconditional image generation experiments with multiple datasets, and show that the proposed method performs comparably to state-of-the-art methods while dramatically improving the sampling efficiency to as few as 16 steps without using any test-time acceleration. The proposed framework can also be seamlessly scaled to 1024 times 1024 high-resolution image generation without resorting to latent hierarchy or multi-stage refinements.

We propose a method for adapting neural networks to distribution shifts at test-time. In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of a test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the efficiency and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results. We end with a discussion on general formulations for handling distribution shifts and our observations from comparing with similar approaches from other domains.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

Model compression aims to reduce the redundancy of deep networks to obtain compact models. Recently, channel pruning has become one of the predominant compression methods to deploy deep models on resource-constrained devices. Most channel pruning methods often use a fixed compression rate for all the layers of the model, which, however, may not be optimal. To address this issue, given a target compression rate for the whole model, one can search for the optimal compression rate for each layer. Nevertheless, these methods perform channel pruning for a specific target compression rate. When we consider multiple compression rates, they have to repeat the channel pruning process multiple times, which is very inefficient yet unnecessary. To address this issue, we propose a Conditional Automated Channel Pruning(CACP) method to obtain the compressed models with different compression rates through single channel pruning process. To this end, we develop a conditional model that takes an arbitrary compression rate as input and outputs the corresponding compressed model. In the experiments, the resultant models with different compression rates consistently outperform the models compressed by existing methods with a channel pruning process for each target compression rate.

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image. However, this native noise space does not possess a convenient structure, and is thus challenging to work with in editing tasks. Here, we propose an alternative latent noise space for DDPM that enables a wide range of editing operations via simple means, and present an inversion method for extracting these edit-friendly noise maps for any given image (real or synthetically generated). As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps. However, they allow perfect reconstruction of any desired image, and simple transformations on them translate into meaningful manipulations of the output image (e.g., shifting, color edits). Moreover, in text-conditional models, fixing those noise maps while changing the text prompt, modifies semantics while retaining structure. We illustrate how this property enables text-based editing of real images via the diverse DDPM sampling scheme (in contrast to the popular non-diverse DDIM inversion). We also show how it can be used within existing diffusion-based editing methods to improve their quality and diversity.

Continuous-valued Autoregressive (AR) image generation models have demonstrated notable superiority over their discrete-token counterparts, showcasing considerable reconstruction quality and higher generation fidelity. However, the computational demands of the autoregressive framework result in significant inference overhead. While speculative decoding has proven effective in accelerating Large Language Models (LLMs), their adaptation to continuous-valued visual autoregressive models remains unexplored. This work generalizes the speculative decoding algorithm from discrete tokens to continuous space. By analyzing the intrinsic properties of output distribution, we establish a tailored acceptance criterion for the diffusion distributions prevalent in such models. To overcome the inconsistency that occurred in speculative decoding output distributions, we introduce denoising trajectory alignment and token pre-filling methods. Additionally, we identify the hard-to-sample distribution in the rejection phase. To mitigate this issue, we propose a meticulous acceptance-rejection sampling method with a proper upper bound, thereby circumventing complex integration. Experimental results show that our continuous speculative decoding achieves a remarkable 2.33times speed-up on off-the-shelf models while maintaining the output distribution. Codes will be available at https://github.com/MarkXCloud/CSpD

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

Deep generative models are becoming a cornerstone of modern machine learning. Recent work on conditional generative adversarial networks has shown that learning complex, high-dimensional distributions over natural images is within reach. While the latest models are able to generate high-fidelity, diverse natural images at high resolution, they rely on a vast quantity of labeled data. In this work we demonstrate how one can benefit from recent work on self- and semi-supervised learning to outperform the state of the art on both unsupervised ImageNet synthesis, as well as in the conditional setting. In particular, the proposed approach is able to match the sample quality (as measured by FID) of the current state-of-the-art conditional model BigGAN on ImageNet using only 10% of the labels and outperform it using 20% of the labels.

We consider the learning from noisy labels (NL) problem which emerges in many real-world applications. In addition to the widely-studied synthetic noise in the NL literature, we also consider the pseudo labels in semi-supervised learning (Semi-SL) as a special case of NL. For both types of noise, we argue that the generalization performance of existing methods is highly coupled with the quality of noisy labels. Therefore, we counter the problem from a novel and unified perspective: learning from the auxiliary clean labels. Specifically, we propose the Rotational-Decoupling Consistency Regularization (RDCR) framework that integrates the consistency-based methods with the self-supervised rotation task to learn noise-tolerant representations. The experiments show that RDCR achieves comparable or superior performance than the state-of-the-art methods under small noise, while outperforms the existing methods significantly when there is large noise.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Detecting test samples drawn sufficiently far away from the training distribution statistically or adversarially is a fundamental requirement for deploying a good classifier in many real-world machine learning applications. However, deep neural networks with the softmax classifier are known to produce highly overconfident posterior distributions even for such abnormal samples. In this paper, we propose a simple yet effective method for detecting any abnormal samples, which is applicable to any pre-trained softmax neural classifier. We obtain the class conditional Gaussian distributions with respect to (low- and upper-level) features of the deep models under Gaussian discriminant analysis, which result in a confidence score based on the Mahalanobis distance. While most prior methods have been evaluated for detecting either out-of-distribution or adversarial samples, but not both, the proposed method achieves the state-of-the-art performances for both cases in our experiments. Moreover, we found that our proposed method is more robust in harsh cases, e.g., when the training dataset has noisy labels or small number of samples. Finally, we show that the proposed method enjoys broader usage by applying it to class-incremental learning: whenever out-of-distribution samples are detected, our classification rule can incorporate new classes well without further training deep models.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation r of the training data, and then fitting a simple (e.g., linear) classifier g to the labels. Specifically, we show that (under the assumptions described below) the generalization gap of such classifiers tends to zero if C(g) ll n, where C(g) is an appropriately-defined measure of the simple classifier g's complexity, and n is the number of training samples. We stress that our bound is independent of the complexity of the representation r. We do not make any structural or conditional-independence assumptions on the representation-learning task, which can use the same training dataset that is later used for classification. Rather, we assume that the training procedure satisfies certain natural noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely hold across many standard architectures. We show that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and MoCo.

We describe a new class of subsampling techniques for CNNs, termed multisampling, that significantly increases the amount of information kept by feature maps through subsampling layers. One version of our method, which we call checkered subsampling, significantly improves the accuracy of state-of-the-art architectures such as DenseNet and ResNet without any additional parameters and, remarkably, improves the accuracy of certain pretrained ImageNet models without any training or fine-tuning. We glean possible insight into the nature of data augmentations and demonstrate experimentally that coarse feature maps are bottlenecking the performance of neural networks in image classification.

Existing private synthetic data generation algorithms are agnostic to downstream tasks. However, end users may have specific requirements that the synthetic data must satisfy. Failure to meet these requirements could significantly reduce the utility of the data for downstream use. We introduce a post-processing technique that improves the utility of the synthetic data with respect to measures selected by the end user, while preserving strong privacy guarantees and dataset quality. Our technique involves resampling from the synthetic data to filter out samples that do not meet the selected utility measures, using an efficient stochastic first-order algorithm to find optimal resampling weights. Through comprehensive numerical experiments, we demonstrate that our approach consistently improves the utility of synthetic data across multiple benchmark datasets and state-of-the-art synthetic data generation algorithms.

Recently, universal waveform generation tasks have been investigated conditioned on various out-of-distribution scenarios. Although GAN-based methods have shown their strength in fast waveform generation, they are vulnerable to train-inference mismatch scenarios such as two-stage text-to-speech. Meanwhile, diffusion-based models have shown their powerful generative performance in other domains; however, they stay out of the limelight due to slow inference speed in waveform generation tasks. Above all, there is no generator architecture that can explicitly disentangle the natural periodic features of high-resolution waveform signals. In this paper, we propose PeriodWave, a novel universal waveform generation model. First, we introduce a period-aware flow matching estimator that can capture the periodic features of the waveform signal when estimating the vector fields. Additionally, we utilize a multi-period estimator that avoids overlaps to capture different periodic features of waveform signals. Although increasing the number of periods can improve the performance significantly, this requires more computational costs. To reduce this issue, we also propose a single period-conditional universal estimator that can feed-forward parallel by period-wise batch inference. Additionally, we utilize discrete wavelet transform to losslessly disentangle the frequency information of waveform signals for high-frequency modeling, and introduce FreeU to reduce the high-frequency noise for waveform generation. The experimental results demonstrated that our model outperforms the previous models both in Mel-spectrogram reconstruction and text-to-speech tasks. All source code will be available at https://github.com/sh-lee-prml/PeriodWave.

The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by computational costs and, therefore, often generate coarse-resolution predictions. Statistical downscaling, including super-resolution methods from deep learning, can provide an efficient method of upsampling low-resolution data. However, despite achieving visually compelling results in some cases, such models frequently violate conservation laws when predicting physical variables. In order to conserve physical quantities, here we introduce methods that guarantee statistical constraints are satisfied by a deep learning downscaling model, while also improving their performance according to traditional metrics. We compare different constraining approaches and demonstrate their applicability across different neural architectures as well as a variety of climate and weather data sets. Besides enabling faster and more accurate climate predictions through downscaling, we also show that our novel methodologies can improve super-resolution for satellite data and natural images data sets.

Conditional sound separation in multi-source audio mixtures without having access to single source sound data during training is a long standing challenge. Existing mix-and-separate based methods suffer from significant performance drop with multi-source training mixtures due to the lack of supervision signal for single source separation cases during training. However, in the case of language-conditional audio separation, we do have access to corresponding text descriptions for each audio mixture in our training data, which can be seen as (rough) representations of the audio samples in the language modality. To this end, in this paper, we propose a generic bi-modal separation framework which can enhance the existing unsupervised frameworks to separate single-source signals in a target modality (i.e., audio) using the easily separable corresponding signals in the conditioning modality (i.e., language), without having access to single-source samples in the target modality during training. We empirically show that this is well within reach if we have access to a pretrained joint embedding model between the two modalities (i.e., CLAP). Furthermore, we propose to incorporate our framework into two fundamental scenarios to enhance separation performance. First, we show that our proposed methodology significantly improves the performance of purely unsupervised baselines by reducing the distribution shift between training and test samples. In particular, we show that our framework can achieve 71% boost in terms of Signal-to-Distortion Ratio (SDR) over the baseline, reaching 97.5% of the supervised learning performance. Second, we show that we can further improve the performance of the supervised learning itself by 17% if we augment it by our proposed weakly-supervised framework, that enables a powerful semi-supervised framework for audio separation.

Diffusion large language models (dLLMs) are compelling alternatives to autoregressive (AR) models because their denoising models operate over the entire sequence. The global planning and iterative refinement features of dLLMs are particularly useful for code generation. However, current training and inference mechanisms for dLLMs in coding are still under-explored. To demystify the decoding behavior of dLLMs and unlock their potential for coding, we systematically investigate their denoising processes and reinforcement learning (RL) methods. We train a 7B dLLM, DiffuCoder, on 130B tokens of code. Using this model as a testbed, we analyze its decoding behavior, revealing how it differs from that of AR models: (1) dLLMs can decide how causal their generation should be without relying on semi-AR decoding, and (2) increasing the sampling temperature diversifies not only token choices but also their generation order. This diversity creates a rich search space for RL rollouts. For RL training, to reduce the variance of token log-likelihood estimates and maintain training efficiency, we propose coupled-GRPO, a novel sampling scheme that constructs complementary mask noise for completions used in training. In our experiments, coupled-GRPO significantly improves DiffuCoder's performance on code generation benchmarks (+4.4\% on EvalPlus) and reduces reliance on AR causal during decoding. Our work provides deeper insight into the machinery of dLLM generation and offers an effective, diffusion-native RL training framework. https://github.com/apple/ml-diffucoder.

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.