Related papers: High-accuracy sampling for diffusion models and lo…

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high…

We propose a method for estimating a log-concave density on $\mathbb R^d$ from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave…

Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on…

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function…

We establish a sharp uniform-in-time error estimate for the Stochastic Gradient Langevin Dynamics (SGLD), which is a widely-used sampling algorithm. Under mild assumptions, we obtain a uniform-in-time $O(\eta^2)$ bound for the KL-divergence…

In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of…

Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…

Efficient sampling from complex and high dimensional target distributions turns out to be a fundamental task in diverse disciplines such as scientific computing, statistics and machine learning. In this paper, we propose a new kind of…

We consider the problem of sampling from a $d$-dimensional log-concave distribution $\pi(\theta) \propto \exp(-f(\theta))$ for $L$-Lipschitz $f$, constrained to a convex body with an efficiently computable self-concordant barrier function,…

Although diffusion models can generate remarkably high-quality samples, they are intrinsically bottlenecked by their expensive iterative sampling procedure. Consistency models (CMs) have recently emerged as a promising diffusion model…

Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Diffusion Probabilistic Models (DPMs) have demonstrated exceptional capability of generating high-quality and diverse images, but their practical application is hindered by the intensive computational cost during inference. The DPM…

We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1 loc difference between the…

Diffusion probabilistic models (DPMs) have shown remarkable performance in high-resolution image synthesis, but their sampling efficiency is still to be desired due to the typically large number of sampling steps. Recent advancements in…

The recent introduction of diffusion models in dataset distillation has shown promising potential in creating compact surrogate datasets for large, high-resolution target datasets, offering improved efficiency and performance over…

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…

We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the first upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on…

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of…

For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher…