2023/12/10 by Sokhna Diarra Mbacke, Mbacke, Sokhna Diarra, Omar Rivasplata +1 · 1 citation
Computer Science · Mathematics · #Applied mathematics #Artificial intelligence #Bounded function #Computer science #Convergence (economics) #Data mining #Diffusion #Discrete mathematics #Distribution (mathematics) #Exponential family #Exponential function #FOS: Computer and information sciences #Function (biology) #Generative Adversarial Networks and Image Synthesis #Generative grammar #Generative model #Geometry #Lebesgue integration #Lebesgue measure #Machine Learning (cs.LG) #Machine Learning in Healthcare #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical proof #Mathematics #Measure (data warehouse) #Physics #Probabilistic logic #Statistics #Upper and lower bounds
paper · pdf · doi:10.48550/arxiv.2312.05989
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 model. Unlike previous works in this field, our result does not make assumptions on the learned score function. Moreover, our bound holds for arbitrary data-generating distributions on bounded instance spaces, even those without a density w.r.t. the Lebesgue measure, and the upper bound does not suffer from exponential dependencies. Our main result builds upon the recent work of Mbacke et al. (2023) and our proofs are elementary.