Related papers: Dimension-free error estimate for diffusion model …
Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through…
This paper studies sampling error bounds for denoising diffusion probabilistic models (DDPMs) in the 2-Wasserstein distance. Our contributions are threefold. (i) Under general Lipschitz-type conditions on the score function and for a broad…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed. We first utilize the Cram\'er-Rao bound to identify the Gaussian setting as a fundamental…
Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target.Recent literature has focused extensively on assessing the error between the…
Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still…
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…
Recently proposed generative models for discrete data, such as Masked Diffusion Models (MDMs), exploit conditional independence approximations to reduce the computational cost of popular Auto-Regressive Models (ARMs), at the price of some…
Diffusion models are one of the most important families of deep generative models. In this note, we derive a quantitative upper bound on the Wasserstein distance between the data-generating distribution and the distribution learned by a…
Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser). Existing convergence analyses of diffusion models typically scale at least linearly with the ambient dimension,…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
We show that every $d$-dimensional probability distribution of bounded support can be generated through deep ReLU networks out of a $1$-dimensional uniform input distribution. What is more, this is possible without incurring a cost - in…
Denoising diffusion probabilistic models (DDPMs) represent a recent advance in generative modelling that has delivered state-of-the-art results across many domains of applications. Despite their success, a rigorous theoretical understanding…
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…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a…
We develop a principled framework for analyzing and designing noise schedules in diffusion models. We show that one can recast this design problem as an optimal control problem, whose state is the Fisher information of the diffusion process…