Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees
2026-06-15 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a method called Diffusion Flow Matching (DFM) used to create things like images by simulating random processes. They focus on understanding how close the method comes to the true result when it is broken down into smaller steps, which was not fully clear before. By assuming some mild mathematical properties, they prove better guarantees for how well the method works, measured using specific ways to compare distributions called KL divergence and 2-Wasserstein distance. Their work improves previous results and applies under reasonable conditions.
Diffusion Flow MatchingGenerative modelingBrownian motionDiscretization errorKullback-Leibler divergence2-Wasserstein distanceScore functionLog-concavityConvergence guaranteesFinite moments
Authors
Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus
Abstract
Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood. In this work, we provide refined and novel convergence guarantees for Brownian motion based DFMs, focusing on the discretization error. Our analysis is conducted under the Kullback-Leibler (KL) divergence and the 2-Wasserstein distance. Under finite-moment conditions and a mild score integrability assumption, we derive KL convergence bounds with improved dimensional dependence compared to prior work, achieving, up to our knowledge, state-of-the-art scaling under minimal conditions. We further extend the analysis to the 2-Wasserstein distance: under an additional first-order score integrability assumption and a weak log-concavity condition, we obtain convergence guarantees with dimensional dependence consistent with the KL case.