A Note on the Convergence of Denoising Diffusion Probabilistic Models

Abstract

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 target distribution and the distribution learned by a diffusion model. Unlike previous works on this topic, our result does not make assumptions on the learned score function. Moreover, our result holds for arbitrary data-generating distributions on bounded instance spaces, even those without a density with respect to Lebesgue measure, and the upper bound does not suffer from exponential dependencies on the ambient space dimension. Our main result builds upon the recent work of Mbacke et al. (2023) and our proofs are elementary.