Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds

Fuente: arXiv
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Autori principali: Arsenyan, Vahan, Vardanyan, Elen, Dalalyan, Arnak
Natura: Preprint
Pubblicazione: 2025
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author Arsenyan, Vahan
Vardanyan, Elen
Dalalyan, Arnak
author_facet Arsenyan, Vahan
Vardanyan, Elen
Dalalyan, Arnak
contents Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guarantees in Wasserstein-2 distance that exhibit two key features: (i) they characterize and quantify the robustness of DDPMs to noisy score estimates, and (ii) they achieve faster convergence rates than previously known results. Furthermore, we observe that the obtained rates match those known in the Gaussian case, implying their optimality.
format Preprint
id arxiv_https___arxiv_org_abs_2506_09681
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
Arsenyan, Vahan
Vardanyan, Elen
Dalalyan, Arnak
Machine Learning
Statistics Theory
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guarantees in Wasserstein-2 distance that exhibit two key features: (i) they characterize and quantify the robustness of DDPMs to noisy score estimates, and (ii) they achieve faster convergence rates than previously known results. Furthermore, we observe that the obtained rates match those known in the Gaussian case, implying their optimality.
title Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
topic Machine Learning
Statistics Theory
url https://arxiv.org/abs/2506.09681