Daily Papers

Style transfer, a pivotal task in image processing, synthesizes visually compelling images by seamlessly blending realistic content with artistic styles, enabling applications in photo editing and creative design. While mainstream training-free diffusion-based methods have greatly advanced style transfer in recent years, their reliance on computationally inversion processes compromises efficiency and introduces visual distortions when inversion is inaccurate. To address these limitations, we propose a novel inversion-free style transfer framework based on dual rectified flows, which tackles the challenge of finding an unknown stylized distribution from two distinct inputs (content and style images), only with forward pass. Our approach predicts content and style trajectories in parallel, then fuses them through a dynamic midpoint interpolation that integrates velocities from both paths while adapting to the evolving stylized image. By jointly modeling the content, style, and stylized distributions, our velocity field design achieves robust fusion and avoids the shortcomings of naive overlays. Attention injection further guides style integration, enhancing visual fidelity, content preservation, and computational efficiency. Extensive experiments demonstrate generalization across diverse styles and content, providing an effective and efficient pipeline for style transfer.

Although diffusion models exhibit impressive generative capabilities, existing methods for stylized image generation based on these models often require textual inversion or fine-tuning with style images, which is time-consuming and limits the practical applicability of large-scale diffusion models. To address these challenges, we propose a novel stylized image generation method leveraging a pre-trained large-scale diffusion model without requiring fine-tuning or any additional optimization, termed as OmniPainter. Specifically, we exploit the self-consistency property of latent consistency models to extract the representative style statistics from reference style images to guide the stylization process. Additionally, we then introduce the norm mixture of self-attention, which enables the model to query the most relevant style patterns from these statistics for the intermediate output content features. This mechanism also ensures that the stylized results align closely with the distribution of the reference style images. Our qualitative and quantitative experimental results demonstrate that the proposed method outperforms state-of-the-art approaches.

Recently, significant progress has been made in text-based motion generation, enabling the generation of diverse and high-quality human motions that conform to textual descriptions. However, it remains challenging to generate fine-grained or stylized motions due to the lack of datasets annotated with detailed textual descriptions. By adopting a divide-and-conquer strategy, we propose a new framework named Fine-Grained Human Motion Diffusion Model (FG-MDM) for human motion generation. Specifically, we first parse previous vague textual annotation into fine-grained description of different body parts by leveraging a large language model (GPT-3.5). We then use these fine-grained descriptions to guide a transformer-based diffusion model. FG-MDM can generate fine-grained and stylized motions even outside of the distribution of the training data. Our experimental results demonstrate the superiority of FG-MDM over previous methods, especially the strong generalization capability. We will release our fine-grained textual annotations for HumanML3D and KIT.

The stylization of 3D scenes is an increasingly attractive topic in 3D vision. Although image style transfer has been extensively researched with promising results, directly applying 2D style transfer methods to 3D scenes often fails to preserve the structural and multi-view properties of 3D environments, resulting in unpleasant distortions in images from different viewpoints. To address these issues, we leverage the remarkable generative prior of diffusion-based models and propose a novel style transfer method, OSDiffST, based on a pre-trained one-step diffusion model (i.e., SD-Turbo) for rendering diverse styles in multi-view images of 3D scenes. To efficiently adapt the pre-trained model for multi-view style transfer on small datasets, we introduce a vision condition module to extract style information from the reference style image to serve as conditional input for the diffusion model and employ LoRA in diffusion model for adaptation. Additionally, we consider color distribution alignment and structural similarity between the stylized and content images using two specific loss functions. As a result, our method effectively preserves the structural information and multi-view consistency in stylized images without any 3D information. Experiments show that our method surpasses other promising style transfer methods in synthesizing various styles for multi-view images of 3D scenes. Stylized images from different viewpoints generated by our method achieve superior visual quality, with better structural integrity and less distortion. The source code is available at https://github.com/YushenZuo/OSDiffST.

Generative modeling of high-frequency limit order book (LOB) dynamics is a critical yet unsolved challenge in quantitative finance, essential for robust market simulation and strategy backtesting. Existing approaches are often constrained by simplifying stochastic assumptions or, in the case of modern deep learning models like Transformers, rely on tokenization schemes that affect the high-precision, numerical nature of financial data through discretization and binning. To address these limitations, we introduce ByteGen, a novel generative model that operates directly on the raw byte streams of LOB events. Our approach treats the problem as an autoregressive next-byte prediction task, for which we design a compact and efficient 32-byte packed binary format to represent market messages without information loss. The core novelty of our work is the complete elimination of feature engineering and tokenization, enabling the model to learn market dynamics from its most fundamental representation. We achieve this by adapting the H-Net architecture, a hybrid Mamba-Transformer model that uses a dynamic chunking mechanism to discover the inherent structure of market messages without predefined rules. Our primary contributions are: 1) the first end-to-end, byte-level framework for LOB modeling; 2) an efficient packed data representation; and 3) a comprehensive evaluation on high-frequency data. Trained on over 34 million events from CME Bitcoin futures, ByteGen successfully reproduces key stylized facts of financial markets, generating realistic price distributions, heavy-tailed returns, and bursty event timing. Our findings demonstrate that learning directly from byte space is a promising and highly flexible paradigm for modeling complex financial systems, achieving competitive performance on standard market quality metrics without the biases of tokenization.

Diffusion-based text-to-image generation models like GLIDE and DALLE-2 have gained wide success recently for their superior performance in turning complex text inputs into images of high quality and wide diversity. In particular, they are proven to be very powerful in creating graphic arts of various formats and styles. Although current models supported specifying style formats like oil painting or pencil drawing, fine-grained style features like color distributions and brush strokes are hard to specify as they are randomly picked from a conditional distribution based on the given text input. Here we propose a novel style guidance method to support generating images using arbitrary style guided by a reference image. The generation method does not require a separate style transfer model to generate desired styles while maintaining image quality in generated content as controlled by the text input. Additionally, the guidance method can be applied without a style reference, denoted as self style guidance, to generate images of more diverse styles. Comprehensive experiments prove that the proposed method remains robust and effective in a wide range of conditions, including diverse graphic art forms, image content types and diffusion models.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

Recent advancements in neural representations, such as Neural Radiance Fields and 3D Gaussian Splatting, have increased interest in applying style transfer to 3D scenes. While existing methods can transfer style patterns onto 3D-consistent neural representations, they struggle to effectively extract and transfer high-level style semantics from the reference style image. Additionally, the stylized results often lack structural clarity and separation, making it difficult to distinguish between different instances or objects within the 3D scene. To address these limitations, we propose a novel 3D style transfer pipeline that effectively integrates prior knowledge from pretrained 2D diffusion models. Our pipeline consists of two key stages: First, we leverage diffusion priors to generate stylized renderings of key viewpoints. Then, we transfer the stylized key views onto the 3D representation. This process incorporates two innovative designs. The first is cross-view style alignment, which inserts cross-view attention into the last upsampling block of the UNet, allowing feature interactions across multiple key views. This ensures that the diffusion model generates stylized key views that maintain both style fidelity and instance-level consistency. The second is instance-level style transfer, which effectively leverages instance-level consistency across stylized key views and transfers it onto the 3D representation. This results in a more structured, visually coherent, and artistically enriched stylization. Extensive qualitative and quantitative experiments demonstrate that our 3D style transfer pipeline significantly outperforms state-of-the-art methods across a wide range of scenes, from forward-facing to challenging 360-degree environments. Visit our project page https://jm-xu.github.io/SSGaussian for immersive visualization.

Score Distillation Sampling (SDS) has emerged as a prevalent technique for text-to-3D generation, enabling 3D content creation by distilling view-dependent information from text-to-2D guidance. However, they frequently exhibit shortcomings such as over-saturated color and excess smoothness. In this paper, we conduct a thorough analysis of SDS and refine its formulation, finding that the core design is to model the distribution of rendered images. Following this insight, we introduce a novel strategy called Variational Distribution Mapping (VDM), which expedites the distribution modeling process by regarding the rendered images as instances of degradation from diffusion-based generation. This special design enables the efficient training of variational distribution by skipping the calculations of the Jacobians in the diffusion U-Net. We also introduce timestep-dependent Distribution Coefficient Annealing (DCA) to further improve distilling precision. Leveraging VDM and DCA, we use Gaussian Splatting as the 3D representation and build a text-to-3D generation framework. Extensive experiments and evaluations demonstrate the capability of VDM and DCA to generate high-fidelity and realistic assets with optimization efficiency.

Recent large-scale diffusion models generate high-quality images but struggle to learn new, personalized artistic styles, which limits the creation of unique style templates. Fine-tuning with reference images is the most promising approach, but it often blindly utilizes objectives and noise level distributions used for pre-training, leading to suboptimal style alignment. We propose the Style-friendly SNR sampler, which aggressively shifts the signal-to-noise ratio (SNR) distribution toward higher noise levels during fine-tuning to focus on noise levels where stylistic features emerge. This enables models to better capture unique styles and generate images with higher style alignment. Our method allows diffusion models to learn and share new "style templates", enhancing personalized content creation. We demonstrate the ability to generate styles such as personal watercolor paintings, minimal flat cartoons, 3D renderings, multi-panel images, and memes with text, thereby broadening the scope of style-driven generation.

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

Recently, the multimedia community has witnessed the rise of diffusion models trained on large-scale multi-modal data for visual content creation, particularly in the field of text-to-image generation. In this paper, we propose a new task for ``stylizing'' text-to-image models, namely text-driven stylized image generation, that further enhances editability in content creation. Given input text prompt and style image, this task aims to produce stylized images which are both semantically relevant to input text prompt and meanwhile aligned with the style image in style. To achieve this, we present a new diffusion model (ControlStyle) via upgrading a pre-trained text-to-image model with a trainable modulation network enabling more conditions of text prompts and style images. Moreover, diffusion style and content regularizations are simultaneously introduced to facilitate the learning of this modulation network with these diffusion priors, pursuing high-quality stylized text-to-image generation. Extensive experiments demonstrate the effectiveness of our ControlStyle in producing more visually pleasing and artistic results, surpassing a simple combination of text-to-image model and conventional style transfer techniques.

Recently, the application of modern diffusion-based text-to-image generation models for creating artistic fonts, traditionally the domain of professional designers, has garnered significant interest. Diverging from the majority of existing studies that concentrate on generating artistic typography, our research aims to tackle a novel and more demanding challenge: the generation of text effects for multilingual fonts. This task essentially requires generating coherent and consistent visual content within the confines of a font-shaped canvas, as opposed to a traditional rectangular canvas. To address this task, we introduce a novel shape-adaptive diffusion model capable of interpreting the given shape and strategically planning pixel distributions within the irregular canvas. To achieve this, we curate a high-quality shape-adaptive image-text dataset and incorporate the segmentation mask as a visual condition to steer the image generation process within the irregular-canvas. This approach enables the traditionally rectangle canvas-based diffusion model to produce the desired concepts in accordance with the provided geometric shapes. Second, to maintain consistency across multiple letters, we also present a training-free, shape-adaptive effect transfer method for transferring textures from a generated reference letter to others. The key insights are building a font effect noise prior and propagating the font effect information in a concatenated latent space. The efficacy of our FontStudio system is confirmed through user preference studies, which show a marked preference (78% win-rates on aesthetics) for our system even when compared to the latest unrivaled commercial product, Adobe Firefly.

Recent advances in Text-to-Image (T2I) diffusion models have transformed image generation, enabling significant progress in stylized generation using only a few style reference images. However, current diffusion-based methods struggle with fine-grained style customization due to challenges in controlling multiple style attributes, such as color and texture. This paper introduces the first tuning-free approach to achieve free-lunch color-texture disentanglement in stylized T2I generation, addressing the need for independently controlled style elements for the Disentangled Stylized Image Generation (DisIG) problem. Our approach leverages the Image-Prompt Additivity property in the CLIP image embedding space to develop techniques for separating and extracting Color-Texture Embeddings (CTE) from individual color and texture reference images. To ensure that the color palette of the generated image aligns closely with the color reference, we apply a whitening and coloring transformation to enhance color consistency. Additionally, to prevent texture loss due to the signal-leak bias inherent in diffusion training, we introduce a noise term that preserves textural fidelity during the Regularized Whitening and Coloring Transformation (RegWCT). Through these methods, our Style Attributes Disentanglement approach (SADis) delivers a more precise and customizable solution for stylized image generation. Experiments on images from the WikiArt and StyleDrop datasets demonstrate that, both qualitatively and quantitatively, SADis surpasses state-of-the-art stylization methods in the DisIG task.Code will be released at https://deepffff.github.io/sadis.github.io/.

We introduce a novel Stylized Motion Diffusion model, dubbed SMooDi, to generate stylized motion driven by content texts and style motion sequences. Unlike existing methods that either generate motion of various content or transfer style from one sequence to another, SMooDi can rapidly generate motion across a broad range of content and diverse styles. To this end, we tailor a pre-trained text-to-motion model for stylization. Specifically, we propose style guidance to ensure that the generated motion closely matches the reference style, alongside a lightweight style adaptor that directs the motion towards the desired style while ensuring realism. Experiments across various applications demonstrate that our proposed framework outperforms existing methods in stylized motion generation.

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.

Stylized text-to-image generation focuses on creating images from textual descriptions while adhering to a style specified by a few reference images. However, subtle style variations within different reference images can hinder the model from accurately learning the target style. In this paper, we propose InstaStyle, a novel approach that excels in generating high-fidelity stylized images with only a single reference image. Our approach is based on the finding that the inversion noise from a stylized reference image inherently carries the style signal, as evidenced by their non-zero signal-to-noise ratio. We employ DDIM inversion to extract this noise from the reference image and leverage a diffusion model to generate new stylized images from the ``style" noise. Additionally, the inherent ambiguity and bias of textual prompts impede the precise conveying of style. To address this, we introduce a learnable style token via prompt refinement, which enhances the accuracy of the style description for the reference image. Qualitative and quantitative experimental results demonstrate that InstaStyle achieves superior performance compared to current benchmarks. Furthermore, our approach also showcases its capability in the creative task of style combination with mixed inversion noise.

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

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.

Innovative visual stylization is a cornerstone of artistic creation, yet generating novel and consistent visual styles remains a significant challenge. Existing generative approaches typically rely on lengthy textual prompts, reference images, or parameter-efficient fine-tuning to guide style-aware image generation, but often struggle with style consistency, limited creativity, and complex style representations. In this paper, we affirm that a style is worth one numerical code by introducing the novel task, code-to-style image generation, which produces images with novel, consistent visual styles conditioned solely on a numerical style code. To date, this field has only been primarily explored by the industry (e.g., Midjourney), with no open-source research from the academic community. To fill this gap, we propose CoTyle, the first open-source method for this task. Specifically, we first train a discrete style codebook from a collection of images to extract style embeddings. These embeddings serve as conditions for a text-to-image diffusion model (T2I-DM) to generate stylistic images. Subsequently, we train an autoregressive style generator on the discrete style embeddings to model their distribution, allowing the synthesis of novel style embeddings. During inference, a numerical style code is mapped to a unique style embedding by the style generator, and this embedding guides the T2I-DM to generate images in the corresponding style. Unlike existing methods, our method offers unparalleled simplicity and diversity, unlocking a vast space of reproducible styles from minimal input. Extensive experiments validate that CoTyle effectively turns a numerical code into a style controller, demonstrating a style is worth one code.

Creating graphic layouts is a fundamental step in graphic designs. In this work, we present a novel generative model named LayoutDiffusion for automatic layout generation. As layout is typically represented as a sequence of discrete tokens, LayoutDiffusion models layout generation as a discrete denoising diffusion process. It learns to reverse a mild forward process, in which layouts become increasingly chaotic with the growth of forward steps and layouts in the neighboring steps do not differ too much. Designing such a mild forward process is however very challenging as layout has both categorical attributes and ordinal attributes. To tackle the challenge, we summarize three critical factors for achieving a mild forward process for the layout, i.e., legality, coordinate proximity and type disruption. Based on the factors, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule. Experiments on RICO and PubLayNet datasets show that LayoutDiffusion outperforms state-of-the-art approaches significantly. Moreover, it enables two conditional layout generation tasks in a plug-and-play manner without re-training and achieves better performance than existing methods.

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness in real-world settings.

Style transfer has been widely applied to give real-world images a new artistic look. However, given a stylized image, the attempts to use typical style transfer methods for de-stylization or transferring it again into another style usually lead to artifacts or undesired results. We realize that these issues are originated from the content inconsistency between the original image and its stylized output. Therefore, in this paper we advance to keep the content information of the input image during the process of style transfer by the power of steganography, with two approaches proposed: a two-stage model and an end-to-end model. We conduct extensive experiments to successfully verify the capacity of our models, in which both of them are able to not only generate stylized images of quality comparable with the ones produced by typical style transfer methods, but also effectively eliminate the artifacts introduced in reconstructing original input from a stylized image as well as performing multiple times of style transfer in series.

Style-guided texture generation aims to generate a texture that is harmonious with both the style of the reference image and the geometry of the input mesh, given a reference style image and a 3D mesh with its text description. Although diffusion-based 3D texture generation methods, such as distillation sampling, have numerous promising applications in stylized games and films, it requires addressing two challenges: 1) decouple style and content completely from the reference image for 3D models, and 2) align the generated texture with the color tone, style of the reference image, and the given text prompt. To this end, we introduce StyleTex, an innovative diffusion-model-based framework for creating stylized textures for 3D models. Our key insight is to decouple style information from the reference image while disregarding content in diffusion-based distillation sampling. Specifically, given a reference image, we first decompose its style feature from the image CLIP embedding by subtracting the embedding's orthogonal projection in the direction of the content feature, which is represented by a text CLIP embedding. Our novel approach to disentangling the reference image's style and content information allows us to generate distinct style and content features. We then inject the style feature into the cross-attention mechanism to incorporate it into the generation process, while utilizing the content feature as a negative prompt to further dissociate content information. Finally, we incorporate these strategies into StyleTex to obtain stylized textures. The resulting textures generated by StyleTex retain the style of the reference image, while also aligning with the text prompts and intrinsic details of the given 3D mesh. Quantitative and qualitative experiments show that our method outperforms existing baseline methods by a significant margin.

We develop an econometric framework integrating heavy-tailed Student's t distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we demonstrate Student's t specifications outperform Gaussian models in 88.4\% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99\% Value-at-Risk by 19.7\% versus 3.2\% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

When the performance of a machine learning model varies over groups defined by sensitive attributes (e.g., gender or ethnicity), the performance disparity can be expressed in terms of the probability distributions of the input and output variables over each group. In this paper, we exploit this fact to reduce the disparate impact of a fixed classification model over a population of interest. Given a black-box classifier, we aim to eliminate the performance gap by perturbing the distribution of input variables for the disadvantaged group. We refer to the perturbed distribution as a counterfactual distribution, and characterize its properties for common fairness criteria. We introduce a descent algorithm to learn a counterfactual distribution from data. We then discuss how the estimated distribution can be used to build a data preprocessor that can reduce disparate impact without training a new model. We validate our approach through experiments on real-world datasets, showing that it can repair different forms of disparity without a significant drop in accuracy.

We propose a credit risk model for portfolios composed of green and brown loans, extending the ASRF framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, CDO pricing, and empirical analysis of green loan portfolios.

In this paper, we investigate the underexplored challenge of sample diversity in autoregressive (AR) generative models with bitwise visual tokenizers. We first analyze the factors that limit diversity in bitwise AR models and identify two key issues: (1) the binary classification nature of bitwise modeling, which restricts the prediction space, and (2) the overly sharp logits distribution, which causes sampling collapse and reduces diversity. Building on these insights, we propose DiverseAR, a principled and effective method that enhances image diversity without sacrificing visual quality. Specifically, we introduce an adaptive logits distribution scaling mechanism that dynamically adjusts the sharpness of the binary output distribution during sampling, resulting in smoother predictions and greater diversity. To mitigate potential fidelity loss caused by distribution smoothing, we further develop an energy-based generation path search algorithm that avoids sampling low-confidence tokens, thereby preserving high visual quality. Extensive experiments demonstrate that DiverseAR substantially improves sample diversity in bitwise autoregressive image generation.

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

Layout design is an important task in various design fields, including user interface, document, and graphic design. As this task requires tedious manual effort by designers, prior works have attempted to automate this process using generative models, but commonly fell short of providing intuitive user controls and achieving design objectives. In this paper, we build a conditional latent diffusion model, PLay, that generates parametrically conditioned layouts in vector graphic space from user-specified guidelines, which are commonly used by designers for representing their design intents in current practices. Our method outperforms prior works across three datasets on metrics including FID and FD-VG, and in user study. Moreover, it brings a novel and interactive experience to professional layout design processes.

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

This paper introduces a novel approach to financial risk analysis that does not rely on traditional price and market data, instead using market news to model assets as distributions over a metric space of risk factors. By representing asset returns as integrals over the scalar field of these risk factors, we derive the covariance structure between asset returns. Utilizing encoder-only language models to embed this news data, we explore the relationships between asset return distributions through the concept of Energy Distance, establishing connections between distributional differences and excess returns co-movements. This data-agnostic approach provides new insights into portfolio diversification, risk management, and the construction of hedging strategies. Our findings have significant implications for both theoretical finance and practical risk management, offering a more robust framework for modelling complex financial systems without depending on conventional market data.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

The popularization of Text-to-Image (T2I) diffusion models enables the generation of high-quality images from text descriptions. However, generating diverse customized images with reference visual attributes remains challenging. This work focuses on personalizing T2I diffusion models at a more abstract concept or category level, adapting commonalities from a set of reference images while creating new instances with sufficient variations. We introduce a solution that allows a pretrained T2I diffusion model to learn a set of soft prompts, enabling the generation of novel images by sampling prompts from the learned distribution. These prompts offer text-guided editing capabilities and additional flexibility in controlling variation and mixing between multiple distributions. We also show the adaptability of the learned prompt distribution to other tasks, such as text-to-3D. Finally we demonstrate effectiveness of our approach through quantitative analysis including automatic evaluation and human assessment. Project website: https://briannlongzhao.github.io/DreamDistribution

Generative models are now widely used by graphic designers and artists. Prior works have shown that these models remember and often replicate content from their training data during generation. Hence as their proliferation increases, it has become important to perform a database search to determine whether the properties of the image are attributable to specific training data, every time before a generated image is used for professional purposes. Existing tools for this purpose focus on retrieving images of similar semantic content. Meanwhile, many artists are concerned with style replication in text-to-image models. We present a framework for understanding and extracting style descriptors from images. Our framework comprises a new dataset curated using the insight that style is a subjective property of an image that captures complex yet meaningful interactions of factors including but not limited to colors, textures, shapes, etc. We also propose a method to extract style descriptors that can be used to attribute style of a generated image to the images used in the training dataset of a text-to-image model. We showcase promising results in various style retrieval tasks. We also quantitatively and qualitatively analyze style attribution and matching in the Stable Diffusion model. Code and artifacts are available at https://github.com/learn2phoenix/CSD.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

Finite symmetric groups S_n are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over S_n poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce SymmetricDiffusers, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over S_n by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performances on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at https://github.com/DSL-Lab/SymmetricDiffusers.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.

Recent advancements in text-to-image models, such as Stable Diffusion, have demonstrated their ability to synthesize visual images through natural language prompts. One approach of personalizing text-to-image models, exemplified by DreamBooth, fine-tunes the pre-trained model by binding unique text identifiers with a few images of a specific subject. Although existing fine-tuning methods have demonstrated competence in rendering images according to the styles of famous painters, it is still challenging to learn to produce images encapsulating distinct art styles due to abstract and broad visual perceptions of stylistic attributes such as lines, shapes, textures, and colors. In this paper, we introduce a new method, Single-StyleForge, for personalization. It fine-tunes pre-trained text-to-image diffusion models to generate diverse images in specified styles from text prompts. By using around 15-20 images of the target style, the approach establishes a foundational binding of a unique token identifier with a broad range of the target style. It also utilizes auxiliary images to strengthen this binding, resulting in offering specific guidance on representing elements such as persons in a target style-consistent manner. In addition, we present ways to improve the quality of style and text-image alignment through a method called Multi-StyleForge, which inherits the strategy used in StyleForge and learns tokens in multiple. Experimental evaluation conducted on six distinct artistic styles demonstrates substantial improvements in both the quality of generated images and the perceptual fidelity metrics, such as FID, KID, and CLIP scores.

A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining and hopefully mitigating the effect of such a shift. Most prior work focuses on merely detecting if a shift has occurred and assumes any detected shift can be understood and handled appropriately by a human operator. We hope to aid in these manual mitigation tasks by explaining the distribution shift using interpretable transportation maps from the original distribution to the shifted one. We derive our interpretable mappings from a relaxation of optimal transport, where the candidate mappings are restricted to a set of interpretable mappings. We then inspect multiple quintessential use-cases of distribution shift in real-world tabular, text, and image datasets to showcase how our explanatory mappings provide a better balance between detail and interpretability than baseline explanations by both visual inspection and our PercentExplained metric.

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

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.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images, videos, audio, 3D shapes, deformations, \etc, can be handled by the same framework with minimal changes. In addition, functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work, we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.

Arbitrary style transfer (AST) and domain generalization (DG) are important yet challenging visual learning tasks, which can be cast as a feature distribution matching problem. With the assumption of Gaussian feature distribution, conventional feature distribution matching methods usually match the mean and standard deviation of features. However, the feature distributions of real-world data are usually much more complicated than Gaussian, which cannot be accurately matched by using only the first-order and second-order statistics, while it is computationally prohibitive to use high-order statistics for distribution matching. In this work, we, for the first time to our best knowledge, propose to perform Exact Feature Distribution Matching (EFDM) by exactly matching the empirical Cumulative Distribution Functions (eCDFs) of image features, which could be implemented by applying the Exact Histogram Matching (EHM) in the image feature space. Particularly, a fast EHM algorithm, named Sort-Matching, is employed to perform EFDM in a plug-and-play manner with minimal cost. The effectiveness of our proposed EFDM method is verified on a variety of AST and DG tasks, demonstrating new state-of-the-art results. Codes are available at https://github.com/YBZh/EFDM.

In contrast to classical reinforcement learning, distributional reinforcement learning algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

Denoising Diffusion Probabilistic Models (DDPMs) exhibit remarkable capabilities in image generation, with studies suggesting that they can generalize by composing latent factors learned from the training data. In this work, we go further and study DDPMs trained on strictly separate subsets of the data distribution with large gaps on the support of the latent factors. We show that such a model can effectively generate images in the unexplored, intermediate regions of the distribution. For instance, when trained on clearly smiling and non-smiling faces, we demonstrate a sampling procedure which can generate slightly smiling faces without reference images (zero-shot interpolation). We replicate these findings for other attributes as well as other datasets. Our code is available at https://github.com/jdeschena/ddpm-zero-shot-interpolation.

Building on recent advances in image generation, we present a fully data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising operations on top of a Gaussian noise distribution. We view the diffusion denoising process as a sequential decision making process, and show that it exhibits compounding errors similar to exposure bias issues in imitation learning problems. To mitigate these issues, we adapt the scheduled sampling algorithm to diffusion training. We conduct experiments on four markup datasets: mathematical formulas (LaTeX), table layouts (HTML), sheet music (LilyPond), and molecular images (SMILES). These experiments each verify the effectiveness of the diffusion process and the use of scheduled sampling to fix generation issues. These results also show that the markup-to-image task presents a useful controlled compositional setting for diagnosing and analyzing generative image models.

Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the second-order polynomial maximization method (PMM2) for estimating ARIMA(p,d,q) models with non-Gaussian innovations. PMM2 is a semiparametric technique that exploits higher-order moments and cumulants without requiring full distributional specification. Monte Carlo experiments (128,000 simulations) across sample sizes N in {100, 200, 500, 1000} and four innovation distributions demonstrate that PMM2 substantially outperforms classical methods for asymmetric innovations. For ARIMA(1,1,0) with N=500, relative efficiency reaches 1.58--1.90 for Gamma, lognormal, and χ^2(3) innovations (37--47\% variance reduction). Under Gaussian innovations PMM2 matches OLS efficiency, avoiding the precision loss typical of robust estimators. The method delivers major gains for moderate asymmetry (|γ_3| geq 0.5) and N geq 200, with computational costs comparable to MLE. PMM2 provides an effective alternative for time series with asymmetric innovations typical of financial markets, macroeconomic indicators, and industrial measurements. Future extensions include seasonal SARIMA models, GARCH integration, and automatic order selection.

Text plays a crucial role in the transmission of human civilization, and teaching machines to generate online handwritten text in various styles presents an interesting and significant challenge. However, most prior work has concentrated on generating individual Chinese fonts, leaving {complete text line generation largely unexplored}. In this paper, we identify that text lines can naturally be divided into two components: layout and glyphs. Based on this division, we designed a text line layout generator coupled with a diffusion-based stylized font synthesizer to address this challenge hierarchically. More concretely, the layout generator performs in-context-like learning based on the text content and the provided style references to generate positions for each glyph autoregressively. Meanwhile, the font synthesizer which consists of a character embedding dictionary, a multi-scale calligraphy style encoder, and a 1D U-Net based diffusion denoiser will generate each font on its position while imitating the calligraphy style extracted from the given style references. Qualitative and quantitative experiments on the CASIA-OLHWDB demonstrate that our method is capable of generating structurally correct and indistinguishable imitation samples.

We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT). The interpolant framework, which allows for connecting two distributions in a more flexible way than standard diffusion models, makes possible a modular study of various design choices impacting generative models built on dynamical transport: using discrete vs. continuous time learning, deciding the objective for the model to learn, choosing the interpolant connecting the distributions, and deploying a deterministic or stochastic sampler. By carefully introducing the above ingredients, SiT surpasses DiT uniformly across model sizes on the conditional ImageNet 256x256 benchmark using the exact same backbone, number of parameters, and GFLOPs. By exploring various diffusion coefficients, which can be tuned separately from learning, SiT achieves an FID-50K score of 2.06.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.

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.

OpenAI's Sora highlights the potential of video generation for developing world models that adhere to fundamental physical laws. However, the ability of video generation models to discover such laws purely from visual data without human priors can be questioned. A world model learning the true law should give predictions robust to nuances and correctly extrapolate on unseen scenarios. In this work, we evaluate across three key scenarios: in-distribution, out-of-distribution, and combinatorial generalization. We developed a 2D simulation testbed for object movement and collisions to generate videos deterministically governed by one or more classical mechanics laws. This provides an unlimited supply of data for large-scale experimentation and enables quantitative evaluation of whether the generated videos adhere to physical laws. We trained diffusion-based video generation models to predict object movements based on initial frames. Our scaling experiments show perfect generalization within the distribution, measurable scaling behavior for combinatorial generalization, but failure in out-of-distribution scenarios. Further experiments reveal two key insights about the generalization mechanisms of these models: (1) the models fail to abstract general physical rules and instead exhibit "case-based" generalization behavior, i.e., mimicking the closest training example; (2) when generalizing to new cases, models are observed to prioritize different factors when referencing training data: color > size > velocity > shape. Our study suggests that scaling alone is insufficient for video generation models to uncover fundamental physical laws, despite its role in Sora's broader success. See our project page at https://phyworld.github.io

This paper introduces a method for realistic kinetic typography that generates user-preferred animatable 'text content'. We draw on recent advances in guided video diffusion models to achieve visually-pleasing text appearances. To do this, we first construct a kinetic typography dataset, comprising about 600K videos. Our dataset is made from a variety of combinations in 584 templates designed by professional motion graphics designers and involves changing each letter's position, glyph, and size (i.e., flying, glitches, chromatic aberration, reflecting effects, etc.). Next, we propose a video diffusion model for kinetic typography. For this, there are three requirements: aesthetic appearances, motion effects, and readable letters. This paper identifies the requirements. For this, we present static and dynamic captions used as spatial and temporal guidance of a video diffusion model, respectively. The static caption describes the overall appearance of the video, such as colors, texture and glyph which represent a shape of each letter. The dynamic caption accounts for the movements of letters and backgrounds. We add one more guidance with zero convolution to determine which text content should be visible in the video. We apply the zero convolution to the text content, and impose it on the diffusion model. Lastly, our glyph loss, only minimizing a difference between the predicted word and its ground-truth, is proposed to make the prediction letters readable. Experiments show that our model generates kinetic typography videos with legible and artistic letter motions based on text prompts.

For an artist or a graphic designer, the spatial layout of a scene is a critical design choice. However, existing text-to-image diffusion models provide limited support for incorporating spatial information. This paper introduces Composite Diffusion as a means for artists to generate high-quality images by composing from the sub-scenes. The artists can specify the arrangement of these sub-scenes through a flexible free-form segment layout. They can describe the content of each sub-scene primarily using natural text and additionally by utilizing reference images or control inputs such as line art, scribbles, human pose, canny edges, and more. We provide a comprehensive and modular method for Composite Diffusion that enables alternative ways of generating, composing, and harmonizing sub-scenes. Further, we wish to evaluate the composite image for effectiveness in both image quality and achieving the artist's intent. We argue that existing image quality metrics lack a holistic evaluation of image composites. To address this, we propose novel quality criteria especially relevant to composite generation. We believe that our approach provides an intuitive method of art creation. Through extensive user surveys, quantitative and qualitative analysis, we show how it achieves greater spatial, semantic, and creative control over image generation. In addition, our methods do not need to retrain or modify the architecture of the base diffusion models and can work in a plug-and-play manner with the fine-tuned models.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals.~Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression.~To preserve the ordering of the continuous-output space, we design a new loss function and make necessary modifications to the CP classification techniques.~Empirical results on many benchmarks shows that this simple approach gives surprisingly good results on many practical problems.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

Text-to-image diffusion models have recently taken center stage as pivotal tools in promoting visual creativity across an array of domains such as comic book artistry, children's literature, game development, and web design. These models harness the power of artificial intelligence to convert textual descriptions into vivid images, thereby enabling artists and creators to bring their imaginative concepts to life with unprecedented ease. However, one of the significant hurdles that persist is the challenge of maintaining consistency in character generation across diverse contexts. Variations in textual prompts, even if minor, can yield vastly different visual outputs, posing a considerable problem in projects that require a uniform representation of characters throughout. In this paper, we introduce a novel framework designed to produce consistent character representations from a single text prompt across diverse settings. Through both quantitative and qualitative analyses, we demonstrate that our framework outperforms existing methods in generating characters with consistent visual identities, underscoring its potential to transform creative industries. By addressing the critical challenge of character consistency, we not only enhance the practical utility of these models but also broaden the horizons for artistic and creative expression.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

Poster design is a critical medium for visual communication. Prior work has explored automatic poster design using deep learning techniques, but these approaches lack text accuracy, user customization, and aesthetic appeal, limiting their applicability in artistic domains such as movies and exhibitions, where both clear content delivery and visual impact are essential. To address these limitations, we present POSTA: a modular framework powered by diffusion models and multimodal large language models (MLLMs) for customized artistic poster generation. The framework consists of three modules. Background Diffusion creates a themed background based on user input. Design MLLM then generates layout and typography elements that align with and complement the background style. Finally, to enhance the poster's aesthetic appeal, ArtText Diffusion applies additional stylization to key text elements. The final result is a visually cohesive and appealing poster, with a fully modular process that allows for complete customization. To train our models, we develop the PosterArt dataset, comprising high-quality artistic posters annotated with layout, typography, and pixel-level stylized text segmentation. Our comprehensive experimental analysis demonstrates POSTA's exceptional controllability and design diversity, outperforming existing models in both text accuracy and aesthetic quality.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

The diffusion model has shown exceptional capabilities in controlled image generation, which has further fueled interest in image style transfer. Existing works mainly focus on training free-based methods (e.g., image inversion) due to the scarcity of specific data. In this study, we present a data construction pipeline for content-style-stylized image triplets that generates and automatically cleanses stylized data triplets. Based on this pipeline, we construct a dataset IMAGStyle, the first large-scale style transfer dataset containing 210k image triplets, available for the community to explore and research. Equipped with IMAGStyle, we propose CSGO, a style transfer model based on end-to-end training, which explicitly decouples content and style features employing independent feature injection. The unified CSGO implements image-driven style transfer, text-driven stylized synthesis, and text editing-driven stylized synthesis. Extensive experiments demonstrate the effectiveness of our approach in enhancing style control capabilities in image generation. Additional visualization and access to the source code can be located on the project page: https://csgo-gen.github.io/.

In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs), which address the curse of dimensionality inherent in high-cardinality data by utilizing the propagation of chaos property of interacting particles. By treating high-cardinality data as a large stochastic system of interacting particles, we develop a novel score-matching method for infinite-dimensional chaotic particle systems and propose an approximation scheme that employs a subdivision strategy for efficient training. Our theoretical and empirical results demonstrate the scalability and effectiveness of MF-CDMs for managing large high-cardinality data structures, such as 3D point clouds.

Large-scale text-to-image generative models have made impressive strides, showcasing their ability to synthesize a vast array of high-quality images. However, adapting these models for artistic image editing presents two significant challenges. Firstly, users struggle to craft textual prompts that meticulously detail visual elements of the input image. Secondly, prevalent models, when effecting modifications in specific zones, frequently disrupt the overall artistic style, complicating the attainment of cohesive and aesthetically unified artworks. To surmount these obstacles, we build the innovative unified framework CreativeSynth, which is based on a diffusion model with the ability to coordinate multimodal inputs and multitask in the field of artistic image generation. By integrating multimodal features with customized attention mechanisms, CreativeSynth facilitates the importation of real-world semantic content into the domain of art through inversion and real-time style transfer. This allows for the precise manipulation of image style and content while maintaining the integrity of the original model parameters. Rigorous qualitative and quantitative evaluations underscore that CreativeSynth excels in enhancing artistic images' fidelity and preserves their innate aesthetic essence. By bridging the gap between generative models and artistic finesse, CreativeSynth becomes a custom digital palette.

Diffusion models have been widely adopted in image generation, producing higher-quality and more diverse samples than generative adversarial networks (GANs). We introduce a latent diffusion model (LDM) for precipitation nowcasting - short-term forecasting based on the latest observational data. The LDM is more stable and requires less computation to train than GANs, albeit with more computationally expensive generation. We benchmark it against the GAN-based Deep Generative Models of Rainfall (DGMR) and a statistical model, PySTEPS. The LDM produces more accurate precipitation predictions, while the comparisons are more mixed when predicting whether the precipitation exceeds predefined thresholds. The clearest advantage of the LDM is that it generates more diverse predictions than DGMR or PySTEPS. Rank distribution tests indicate that the distribution of samples from the LDM accurately reflects the uncertainty of the predictions. Thus, LDMs are promising for any applications where uncertainty quantification is important, such as weather and climate.

Masked language models (MLM) do not explicitly define a distribution over language, i.e., they are not language models per se. However, recent work has implicitly treated them as such for the purposes of generation and scoring. This paper studies methods for deriving explicit joint distributions from MLMs, focusing on distributions over two tokens, which makes it possible to calculate exact distributional properties. We find that an approach based on identifying joints whose conditionals are closest to those of the MLM works well and outperforms existing Markov random field-based approaches. We further find that this derived model's conditionals can even occasionally outperform the original MLM's conditionals.

Understanding the performance of machine learning (ML) models across diverse data distributions is critically important for reliable applications. Despite recent empirical studies positing a near-perfect linear correlation between in-distribution (ID) and out-of-distribution (OOD) accuracies, we empirically demonstrate that this correlation is more nuanced under subpopulation shifts. Through rigorous experimentation and analysis across a variety of datasets, models, and training epochs, we demonstrate that OOD performance often has a nonlinear correlation with ID performance in subpopulation shifts. Our findings, which contrast previous studies that have posited a linear correlation in model performance during distribution shifts, reveal a "moon shape" correlation (parabolic uptrend curve) between the test performance on the majority subpopulation and the minority subpopulation. This non-trivial nonlinear correlation holds across model architectures, hyperparameters, training durations, and the imbalance between subpopulations. Furthermore, we found that the nonlinearity of this "moon shape" is causally influenced by the degree of spurious correlations in the training data. Our controlled experiments show that stronger spurious correlation in the training data creates more nonlinear performance correlation. We provide complementary experimental and theoretical analyses for this phenomenon, and discuss its implications for ML reliability and fairness. Our work highlights the importance of understanding the nonlinear effects of model improvement on performance in different subpopulations, and has the potential to inform the development of more equitable and responsible machine learning models.

We introduce StyleMM, a novel framework that can construct a stylized 3D Morphable Model (3DMM) based on user-defined text descriptions specifying a target style. Building upon a pre-trained mesh deformation network and a texture generator for original 3DMM-based realistic human faces, our approach fine-tunes these models using stylized facial images generated via text-guided image-to-image (i2i) translation with a diffusion model, which serve as stylization targets for the rendered mesh. To prevent undesired changes in identity, facial alignment, or expressions during i2i translation, we introduce a stylization method that explicitly preserves the facial attributes of the source image. By maintaining these critical attributes during image stylization, the proposed approach ensures consistent 3D style transfer across the 3DMM parameter space through image-based training. Once trained, StyleMM enables feed-forward generation of stylized face meshes with explicit control over shape, expression, and texture parameters, producing meshes with consistent vertex connectivity and animatability. Quantitative and qualitative evaluations demonstrate that our approach outperforms state-of-the-art methods in terms of identity-level facial diversity and stylization capability. The code and videos are available at [kwanyun.github.io/stylemm_page](kwanyun.github.io/stylemm_page).

Customer Lifetime Value (CLTV) prediction is a critical task in business applications. Accurately predicting CLTV is challenging in real-world business scenarios, as the distribution of CLTV is complex and mutable. Firstly, there is a large number of users without any consumption consisting of a long-tailed part that is too complex to fit. Secondly, the small set of high-value users spent orders of magnitude more than a typical user leading to a wide range of the CLTV distribution which is hard to capture in a single distribution. Existing approaches for CLTV estimation either assume a prior probability distribution and fit a single group of distribution-related parameters for all samples, or directly learn from the posterior distribution with manually predefined buckets in a heuristic manner. However, all these methods fail to handle complex and mutable distributions. In this paper, we propose a novel optimal distribution selection model OptDist for CLTV prediction, which utilizes an adaptive optimal sub-distribution selection mechanism to improve the accuracy of complex distribution modeling. Specifically, OptDist trains several candidate sub-distribution networks in the distribution learning module (DLM) for modeling the probability distribution of CLTV. Then, a distribution selection module (DSM) is proposed to select the sub-distribution for each sample, thus making the selection automatically and adaptively. Besides, we design an alignment mechanism that connects both modules, which effectively guides the optimization. We conduct extensive experiments on both two public and one private dataset to verify that OptDist outperforms state-of-the-art baselines. Furthermore, OptDist has been deployed on a large-scale financial platform for customer acquisition marketing campaigns and the online experiments also demonstrate the effectiveness of OptDist.

The increased demand for 3D data in AR/VR, robotics and gaming applications, gave rise to powerful generative pipelines capable of synthesizing high-quality 3D objects. Most of these models rely on the Score Distillation Sampling (SDS) algorithm to optimize a 3D representation such that the rendered image maintains a high likelihood as evaluated by a pre-trained diffusion model. However, finding a correct mode in the high-dimensional distribution produced by the diffusion model is challenging and often leads to issues such as over-saturation, over-smoothing, and Janus-like artifacts. In this paper, we propose a novel learning paradigm for 3D synthesis that utilizes pre-trained diffusion models. Instead of focusing on mode-seeking, our method directly models the distribution discrepancy between multi-view renderings and diffusion priors in an adversarial manner, which unlocks the generation of high-fidelity and photorealistic 3D content, conditioned on a single image and prompt. Moreover, by harnessing the latent space of GANs and expressive diffusion model priors, our method facilitates a wide variety of 3D applications including single-view reconstruction, high diversity generation and continuous 3D interpolation in the open domain. The experiments demonstrate the superiority of our pipeline compared to previous works in terms of generation quality and diversity.

In this work, we focus on synthesizing high-quality textures on 3D meshes. We present Point-UV diffusion, a coarse-to-fine pipeline that marries the denoising diffusion model with UV mapping to generate 3D consistent and high-quality texture images in UV space. We start with introducing a point diffusion model to synthesize low-frequency texture components with our tailored style guidance to tackle the biased color distribution. The derived coarse texture offers global consistency and serves as a condition for the subsequent UV diffusion stage, aiding in regularizing the model to generate a 3D consistent UV texture image. Then, a UV diffusion model with hybrid conditions is developed to enhance the texture fidelity in the 2D UV space. Our method can process meshes of any genus, generating diversified, geometry-compatible, and high-fidelity textures. Code is available at https://cvmi-lab.github.io/Point-UV-Diffusion

Creating visually appealing advertising images is often a labor-intensive and time-consuming process. Is it possible to automatically generate such images using only basic product information--specifically, a product foreground image, taglines, and a target size? Existing methods mainly focus on parts of the problem and fail to provide a comprehensive solution. To address this gap, we propose a novel multistage framework called Product-Centric Advertising Image Design (PAID). It consists of four sequential stages to highlight product foregrounds and taglines while achieving overall image aesthetics: prompt generation, layout generation, background image generation, and graphics rendering. Different expert models are designed and trained for the first three stages: First, we use a visual language model (VLM) to generate background prompts that match the products. Next, a VLM-based layout generation model arranges the placement of product foregrounds, graphic elements (taglines and decorative underlays), and various nongraphic elements (objects from the background prompt). Following this, we train an SDXL-based image generation model that can simultaneously accept prompts, layouts, and foreground controls. To support the PAID framework, we create corresponding datasets with over 50,000 labeled images. Extensive experimental results and online A/B tests demonstrate that PAID can produce more visually appealing advertising images.

What constitutes the "vibe" of a particular scene? What should one find in "a busy, dirty city street", "an idyllic countryside", or "a crime scene in an abandoned living room"? The translation from abstract scene descriptions to stylized scene elements cannot be done with any generality by extant systems trained on rigid and limited indoor datasets. In this paper, we propose to leverage the knowledge captured by foundation models to accomplish this translation. We present a system that can serve as a tool to generate stylized assets for 3D scenes described by a short phrase, without the need to enumerate the objects to be found within the scene or give instructions on their appearance. Additionally, it is robust to open-world concepts in a way that traditional methods trained on limited data are not, affording more creative freedom to the 3D artist. Our system demonstrates this using a foundation model "team" composed of a large language model, a vision-language model and several image diffusion models, which communicate using an interpretable and user-editable intermediate representation, thus allowing for more versatile and controllable stylized asset generation for 3D artists. We introduce novel metrics for this task, and show through human evaluations that in 91% of the cases, our system outputs are judged more faithful to the semantics of the input scene description than the baseline, thus highlighting the potential of this approach to radically accelerate the 3D content creation process for 3D artists.

A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION dataset.

Scalable Vector Graphics (SVGs) are highly favored by designers due to their resolution independence and well-organized layer structure. Although existing text-to-vector (T2V) generation methods can create SVGs from text prompts, they often overlook an important need in practical applications: style customization, which is vital for producing a collection of vector graphics with consistent visual appearance and coherent aesthetics. Extending existing T2V methods for style customization poses certain challenges. Optimization-based T2V models can utilize the priors of text-to-image (T2I) models for customization, but struggle with maintaining structural regularity. On the other hand, feed-forward T2V models can ensure structural regularity, yet they encounter difficulties in disentangling content and style due to limited SVG training data. To address these challenges, we propose a novel two-stage style customization pipeline for SVG generation, making use of the advantages of both feed-forward T2V models and T2I image priors. In the first stage, we train a T2V diffusion model with a path-level representation to ensure the structural regularity of SVGs while preserving diverse expressive capabilities. In the second stage, we customize the T2V diffusion model to different styles by distilling customized T2I models. By integrating these techniques, our pipeline can generate high-quality and diverse SVGs in custom styles based on text prompts in an efficient feed-forward manner. The effectiveness of our method has been validated through extensive experiments. The project page is https://customsvg.github.io.

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects; externally valid treatment choice via robust welfare functions; Wasserstein distributionally robust estimation under data combination; and evaluation of the worst aggregate risk measures.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

Handwritten Text Generation (HTG) conditioned on text and style is a challenging task due to the variability of inter-user characteristics and the unlimited combinations of characters that form new words unseen during training. Diffusion Models have recently shown promising results in HTG but still remain under-explored. We present DiffusionPen (DiffPen), a 5-shot style handwritten text generation approach based on Latent Diffusion Models. By utilizing a hybrid style extractor that combines metric learning and classification, our approach manages to capture both textual and stylistic characteristics of seen and unseen words and styles, generating realistic handwritten samples. Moreover, we explore several variation strategies of the data with multi-style mixtures and noisy embeddings, enhancing the robustness and diversity of the generated data. Extensive experiments using IAM offline handwriting database show that our method outperforms existing methods qualitatively and quantitatively, and its additional generated data can improve the performance of Handwriting Text Recognition (HTR) systems. The code is available at: https://github.com/koninik/DiffusionPen.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

In economy, markets are denoted as efficient when it is impossible to systematically generate profits which outperform the average. In the past years, the concept has been tested in other domains such as the growing sports betting market. Surprisingly, despite its large size and its level of maturity, sports betting shows traits of inefficiency. The anomalies indicate the existence of strategies which shift betting from a game of chance towards a game of skill. This article shows an example for an inefficiency detected in the German soccer betting TOTO 13er Wette, which is operated by state-run lottery agencies. Gamblers have to guess the outcome (win, draw, loss) of 13 soccer matches listed on a lottery tip. Applying stochastic methods, a recipe is presented to determine hit rates for single match outcomes. More important, the recipe provides the number of lottery tips required to achieve a specific number of strikes (number of correct match forecasts per lottery tip) for any given level of safety. An approximation is derived to cope with large numbers in hypergeometric distributions, valid under certain constraints. Overall, the strategy does lead to returns exceeding the aggregated lottery fees, resulting in moderate, but consistent profits. It is briefly discussed if lessions learned from soccer betting can be transferred back to financial markets, because gamblers and retail investors face similar challenges and opportunities.

The study conducted by Shumailov et al. (2024) demonstrates that repeatedly training a generative model on synthetic data leads to model collapse. This finding has generated considerable interest and debate, particularly given that current models have nearly exhausted the available data. In this work, we investigate the effects of fitting a distribution (through Kernel Density Estimation, or KDE) or a model to the data, followed by repeated sampling from it. Our objective is to develop a theoretical understanding of the phenomenon observed by Shumailov et al. (2024). Our results indicate that the outcomes reported are a statistical phenomenon and may be unavoidable.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

We present a new way to merge any two point distribution approaches using distance fields. Our new process allows us to produce digital stippling that fills areas with stipple dots without visual artifacts as well as includes clear linear features without fussiness. Our merging thus benefits from past work that can optimize for either goal individually, yet typically by sacrificing the other. The new possibility of combining any two distributions using different distance field functions and their parameters also allows us to produce a vast range of stippling styles, which we demonstrate as well.

As black-box models increasingly power high-stakes applications, a variety of data-driven explanation methods have been introduced. Meanwhile, machine learning models are constantly challenged by distributional shifts. A question naturally arises: Are data-driven explanations robust against out-of-distribution data? Our empirical results show that even though predict correctly, the model might still yield unreliable explanations under distributional shifts. How to develop robust explanations against out-of-distribution data? To address this problem, we propose an end-to-end model-agnostic learning framework Distributionally Robust Explanations (DRE). The key idea is, inspired by self-supervised learning, to fully utilizes the inter-distribution information to provide supervisory signals for the learning of explanations without human annotation. Can robust explanations benefit the model's generalization capability? We conduct extensive experiments on a wide range of tasks and data types, including classification and regression on image and scientific tabular data. Our results demonstrate that the proposed method significantly improves the model's performance in terms of explanation and prediction robustness against distributional shifts.

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.

Diffusion models have shown impressive results in text-to-image synthesis. Using massive datasets of captioned images, diffusion models learn to generate raster images of highly diverse objects and scenes. However, designers frequently use vector representations of images like Scalable Vector Graphics (SVGs) for digital icons or art. Vector graphics can be scaled to any size, and are compact. We show that a text-conditioned diffusion model trained on pixel representations of images can be used to generate SVG-exportable vector graphics. We do so without access to large datasets of captioned SVGs. By optimizing a differentiable vector graphics rasterizer, our method, VectorFusion, distills abstract semantic knowledge out of a pretrained diffusion model. Inspired by recent text-to-3D work, we learn an SVG consistent with a caption using Score Distillation Sampling. To accelerate generation and improve fidelity, VectorFusion also initializes from an image sample. Experiments show greater quality than prior work, and demonstrate a range of styles including pixel art and sketches. See our project webpage at https://ajayj.com/vectorfusion .

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Meta-learning has emerged as an effective methodology to model several real-world tasks and problems due to its extraordinary effectiveness in the low-data regime. There are many scenarios ranging from the classification of rare diseases to language modelling of uncommon languages where the availability of large datasets is rare. Similarly, for more broader scenarios like self-driving, an autonomous vehicle needs to be trained to handle every situation well. This requires training the ML model on a variety of tasks with good quality data. But often times, we find that the data distribution across various tasks is skewed, i.e.the data follows a long-tail distribution. This leads to the model performing well on some tasks and not performing so well on others leading to model robustness issues. Meta-learning has recently emerged as a potential learning paradigm which can effectively learn from one task and generalize that learning to unseen tasks. In this study, we aim to exploit external knowledge of task relations to improve training stability via effective mini-batching of tasks. We hypothesize that selecting a diverse set of tasks in a mini-batch will lead to a better estimate of the full gradient and hence will lead to a reduction of noise in training.

We present InterHandGen, a novel framework that learns the generative prior of two-hand interaction. Sampling from our model yields plausible and diverse two-hand shapes in close interaction with or without an object. Our prior can be incorporated into any optimization or learning methods to reduce ambiguity in an ill-posed setup. Our key observation is that directly modeling the joint distribution of multiple instances imposes high learning complexity due to its combinatorial nature. Thus, we propose to decompose the modeling of joint distribution into the modeling of factored unconditional and conditional single instance distribution. In particular, we introduce a diffusion model that learns the single-hand distribution unconditional and conditional to another hand via conditioning dropout. For sampling, we combine anti-penetration and classifier-free guidance to enable plausible generation. Furthermore, we establish the rigorous evaluation protocol of two-hand synthesis, where our method significantly outperforms baseline generative models in terms of plausibility and diversity. We also demonstrate that our diffusion prior can boost the performance of two-hand reconstruction from monocular in-the-wild images, achieving new state-of-the-art accuracy.

Arbitrary Style Transfer (AST) aims to transform images by adopting the style from any selected artwork. Nonetheless, the need to accommodate diverse and subjective user preferences poses a significant challenge. While some users wish to preserve distinct content structures, others might favor a more pronounced stylization. Despite advances in feed-forward AST methods, their limited customizability hinders their practical application. We propose a new approach, ArtFusion, which provides a flexible balance between content and style. In contrast to traditional methods reliant on biased similarity losses, ArtFusion utilizes our innovative Dual Conditional Latent Diffusion Probabilistic Models (Dual-cLDM). This approach mitigates repetitive patterns and enhances subtle artistic aspects like brush strokes and genre-specific features. Despite the promising results of conditional diffusion probabilistic models (cDM) in various generative tasks, their introduction to style transfer is challenging due to the requirement for paired training data. ArtFusion successfully navigates this issue, offering more practical and controllable stylization. A key element of our approach involves using a single image for both content and style during model training, all the while maintaining effective stylization during inference. ArtFusion outperforms existing approaches on outstanding controllability and faithful presentation of artistic details, providing evidence of its superior style transfer capabilities. Furthermore, the Dual-cLDM utilized in ArtFusion carries the potential for a variety of complex multi-condition generative tasks, thus greatly broadening the impact of our research.

Zipf's law appears in many application areas but does not have a closed form expression, which may make its use cumbersome. Since it coincides with the truncated version of the Zeta distribution, in this paper we propose three approximate closed form expressions for the truncated Zeta distribution, which may be employed for Zipf's law as well. The three approximations are based on the replacement of the sum occurring in Zipf's law with an integral, and are named respectively the integral approximation, the average integral approximation, and the trapezoidal approximation. While the first one is shown to be of little use, the trapezoidal approximation exhibits an error which is typically lower than 1\%, but is as low as 0.1\% for the range of values of the Zipf parameter below 1.

Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a wide variety of geometries or conformations. The resulting distribution on geometries p(x) is known as the Boltzmann distribution, and many molecular properties are expectations computed under this distribution. Generating accurate samples from the Boltzmann distribution is therefore essential for computing these expectations accurately. Traditional sampling-based methods are computationally expensive, and most recent machine learning-based methods have focused on identifying modes in this distribution rather than generating true samples. Generating such samples requires capturing conformational variability, and it has been widely recognized that the majority of conformational variability in molecules arises from rotatable bonds. In this work, we present VonMisesNet, a new graph neural network that captures conformational variability via a variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions. We demonstrate that VonMisesNet can generate conformations for arbitrary molecules in a way that is both physically accurate with respect to the Boltzmann distribution and orders of magnitude faster than existing sampling methods.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Generating visual layouts is an essential ingredient of graphic design. The ability to condition layout generation on a partial subset of component attributes is critical to real-world applications that involve user interaction. Recently, diffusion models have demonstrated high-quality generative performances in various domains. However, it is unclear how to apply diffusion models to the natural representation of layouts which consists of a mix of discrete (class) and continuous (location, size) attributes. To address the conditioning layout generation problem, we introduce DLT, a joint discrete-continuous diffusion model. DLT is a transformer-based model which has a flexible conditioning mechanism that allows for conditioning on any given subset of all the layout component classes, locations, and sizes. Our method outperforms state-of-the-art generative models on various layout generation datasets with respect to different metrics and conditioning settings. Additionally, we validate the effectiveness of our proposed conditioning mechanism and the joint continuous-diffusion process. This joint process can be incorporated into a wide range of mixed discrete-continuous generative tasks.

A generative adversarial network (GAN) has been a representative backbone model in generative artificial intelligence (AI) because of its powerful performance in capturing intricate data-generating processes. However, the GAN training is well-known for its notorious training instability, usually characterized by the occurrence of mode collapse. Through the lens of gradients' variance, this work particularly analyzes the training instability and inefficiency in the presence of mode collapse by linking it to multimodality in the target distribution. To ease the raised training issues from severe multimodality, we introduce a novel GAN training framework that leverages a series of tempered distributions produced via convex interpolation. With our newly developed GAN objective function, the generator can learn all the tempered distributions simultaneously, conceptually resonating with the parallel tempering in Statistics. Our simulation studies demonstrate the superiority of our approach over existing popular training strategies in both image and tabular data synthesis. We theoretically analyze that such significant improvement can arise from reducing the variance of gradient estimates by using the tempered distributions. Finally, we further develop a variant of the proposed framework aimed at generating fair synthetic data which is one of the growing interests in the field of trustworthy AI.

Many real-world problems require reasoning across multiple scales, demanding models which operate not on single data points, but on entire distributions. We introduce generative distribution embeddings (GDE), a framework that lifts autoencoders to the space of distributions. In GDEs, an encoder acts on sets of samples, and the decoder is replaced by a generator which aims to match the input distribution. This framework enables learning representations of distributions by coupling conditional generative models with encoder networks which satisfy a criterion we call distributional invariance. We show that GDEs learn predictive sufficient statistics embedded in the Wasserstein space, such that latent GDE distances approximately recover the W_2 distance, and latent interpolation approximately recovers optimal transport trajectories for Gaussian and Gaussian mixture distributions. We systematically benchmark GDEs against existing approaches on synthetic datasets, demonstrating consistently stronger performance. We then apply GDEs to six key problems in computational biology: learning representations of cell populations from lineage-tracing data (150K cells), predicting perturbation effects on single-cell transcriptomes (1M cells), predicting perturbation effects on cellular phenotypes (20M single-cell images), modeling tissue-specific DNA methylation patterns (253M sequences), designing synthetic yeast promoters (34M sequences), and spatiotemporal modeling of viral protein sequences (1M sequences).

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.

Developing generative models to create or conditionally create symbolic music presents unique challenges due to the combination of limited data availability and the need for high precision in note pitch. To address these challenges, we introduce an efficient Fine-Grained Guidance (FGG) approach within diffusion models. FGG guides the diffusion models to generate music that aligns more closely with the control and intent of expert composers, which is critical to improve the accuracy, listenability, and quality of generated music. This approach empowers diffusion models to excel in advanced applications such as improvisation, and interactive music creation. We derive theoretical characterizations for both the challenges in symbolic music generation and the effects of the FGG approach. We provide numerical experiments and subjective evaluation to demonstrate the effectiveness of our approach. We have published a demo page to showcase performances, as one of the first in the symbolic music literature's demo pages that enables real-time interactive generation.

Understanding how machine learning models respond to distributional shifts is a key research challenge. Mazes serve as an excellent testbed due to varied generation algorithms offering a nuanced platform to simulate both subtle and pronounced distributional shifts. To enable systematic investigations of model behavior on out-of-distribution data, we present maze-dataset, a comprehensive library for generating, processing, and visualizing datasets consisting of maze-solving tasks. With this library, researchers can easily create datasets, having extensive control over the generation algorithm used, the parameters fed to the algorithm of choice, and the filters that generated mazes must satisfy. Furthermore, it supports multiple output formats, including rasterized and text-based, catering to convolutional neural networks and autoregressive transformer models. These formats, along with tools for visualizing and converting between them, ensure versatility and adaptability in research applications.

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.

Although recent text-to-image (T2I) diffusion models excel at aligning generated images with textual prompts, controlling the visual style of the output remains a challenging task. In this work, we propose Style-Prompting Guidance (SPG), a novel sampling strategy for style-specific image generation. SPG constructs a style noise vector and leverages its directional deviation from unconditional noise to guide the diffusion process toward the target style distribution. By integrating SPG with Classifier-Free Guidance (CFG), our method achieves both semantic fidelity and style consistency. SPG is simple, robust, and compatible with controllable frameworks like ControlNet and IPAdapter, making it practical and widely applicable. Extensive experiments demonstrate the effectiveness and generality of our approach compared to state-of-the-art methods. Code is available at https://github.com/Rumbling281441/SPG.

Deep generative models are routinely used in generating samples from complex, high-dimensional distributions. Despite their apparent successes, their statistical properties are not well understood. A common assumption is that with enough training data and sufficiently large neural networks, deep generative model samples will have arbitrarily small errors in sampling from any continuous target distribution. We set up a unifying framework that debunks this belief. We demonstrate that broad classes of deep generative models, including variational autoencoders and generative adversarial networks, are not universal generators. Under the predominant case of Gaussian latent variables, these models can only generate concentrated samples that exhibit light tails. Using tools from concentration of measure and convex geometry, we give analogous results for more general log-concave and strongly log-concave latent variable distributions. We extend our results to diffusion models via a reduction argument. We use the Gromov--Levy inequality to give similar guarantees when the latent variables lie on manifolds with positive Ricci curvature. These results shed light on the limited capacity of common deep generative models to handle heavy tails. We illustrate the empirical relevance of our work with simulations and financial data.

Recently, 3D generative models have made impressive progress, enabling the generation of almost arbitrary 3D assets from text or image inputs. However, these approaches generate objects in isolation without any consideration for the scene where they will eventually be placed. In this paper, we propose a framework that allows for the stylization of an existing 3D asset to fit into a given 2D scene, and additionally produce a photorealistic composition as if the asset was placed within the environment. This not only opens up a new level of control for object stylization, for example, the same assets can be stylized to reflect changes in the environment, such as summer to winter or fantasy versus futuristic settings-but also makes the object-scene composition more controllable. We achieve this by combining modeling and optimizing the object's texture and environmental lighting through differentiable ray tracing with image priors from pre-trained text-to-image diffusion models. We demonstrate that our method is applicable to a wide variety of indoor and outdoor scenes and arbitrary objects.

Toon shading is a type of non-photorealistic rendering task of animation. Its primary purpose is to render objects with a flat and stylized appearance. As diffusion models have ascended to the forefront of image synthesis methodologies, this paper delves into an innovative form of toon shading based on diffusion models, aiming to directly render photorealistic videos into anime styles. In video stylization, extant methods encounter persistent challenges, notably in maintaining consistency and achieving high visual quality. In this paper, we model the toon shading problem as four subproblems: stylization, consistency enhancement, structure guidance, and colorization. To address the challenges in video stylization, we propose an effective toon shading approach called Diffutoon. Diffutoon is capable of rendering remarkably detailed, high-resolution, and extended-duration videos in anime style. It can also edit the content according to prompts via an additional branch. The efficacy of Diffutoon is evaluated through quantitive metrics and human evaluation. Notably, Diffutoon surpasses both open-source and closed-source baseline approaches in our experiments. Our work is accompanied by the release of both the source code and example videos on Github (Project page: https://ecnu-cilab.github.io/DiffutoonProjectPage/).

Most visual generative models compress images into a latent space before applying diffusion or autoregressive modelling. Yet, existing approaches such as VAEs and foundation model aligned encoders implicitly constrain the latent space without explicitly shaping its distribution, making it unclear which types of distributions are optimal for modeling. We introduce Distribution-Matching VAE (DMVAE), which explicitly aligns the encoder's latent distribution with an arbitrary reference distribution via a distribution matching constraint. This generalizes beyond the Gaussian prior of conventional VAEs, enabling alignment with distributions derived from self-supervised features, diffusion noise, or other prior distributions. With DMVAE, we can systematically investigate which latent distributions are more conducive to modeling, and we find that SSL-derived distributions provide an excellent balance between reconstruction fidelity and modeling efficiency, reaching gFID equals 3.2 on ImageNet with only 64 training epochs. Our results suggest that choosing a suitable latent distribution structure (achieved via distribution-level alignment), rather than relying on fixed priors, is key to bridging the gap between easy-to-model latents and high-fidelity image synthesis. Code is avaliable at https://github.com/sen-ye/dmvae.