Related papers: On the Robustness of Langevin Dynamics to Score Fu…

Motivated by the increasingly popular Score-based Generative Modeling (SGM), we study the Inexact Langevin Dynamics (ILD) and Inexact Langevin Algorithm (ILA) where a score function estimate is used in place of the exact score. We establish…

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…

Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…

Diffusion models are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation. Subsequent to its acquisition, the approximated score function is then…

In this work we study the diffusion annealed Langevin dynamics, a score-based diffusion process recently introduced in the theory of generative models and which is an alternative to the classical overdamped Langevin diffusion. Our goal is…

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate…

Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on…

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…

Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data,…

Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift…

We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is…

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/score-based models have emerged as powerful generative models, capable of generating high-quality samples that mimic the training data distribution. However, it has been observed that they are prone to reproducing training…

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

Geometric tempering is a popular approach to sampling from challenging multi-modal probability distributions by instead sampling from a sequence of distributions which interpolate, using the geometric mean, between an easier proposal…