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We develop a rigorous and general framework for constructing information-theoretic divergences that subsume both $f$-divergences and integral probability metrics (IPMs), such as the $1$-Wasserstein distance. We prove under which assumptions…
Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…
Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…
In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…
Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking.…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…
Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…
We study how well generative adversarial networks (GAN) learn probability distributions from finite samples by analyzing the convergence rates of these models. Our analysis is based on a new oracle inequality that decomposes the estimation…
Diffusion-based generative models are machine learning models that use diffusion processes to learn the probability distribution of high-dimensional data. In recent years, they have become extremely successful in generating multimedia…
Score-based diffusion models have emerged as effective approaches for both conditional and unconditional generation. Still conditional generation is based on either a specific training of a conditional model or classifier guidance, which…
In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation…
Recent work has explored a range of model families for human motion generation, including Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and diffusion-based models. Despite their differences, many methods rely on…
Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…
The diffusion probabilistic generative models are widely used to generate high-quality data. Though they can synthetic data that does not exist in the training set, the rationale behind such generalization is still unexplored. In this…
Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…
Minimum distance estimation (MDE) gained recent attention as a formulation of (implicit) generative modeling. It considers minimizing, over model parameters, a statistical distance between the empirical data distribution and the model. This…