Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees
For practitioners and theorists in generative modeling, this paper improves theoretical understanding of DFM convergence, but the results are incremental as they extend existing analysis frameworks.
This work provides refined convergence guarantees for Brownian motion based Diffusion Flow Matching, achieving state-of-the-art KL divergence bounds with improved dimensional dependence and novel Wasserstein guarantees under mild conditions.
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.