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.

翻译：扩散流匹配（DFM）近期已成为生成建模领域一个通用框架，但其理论收敛性质仍仅被部分理解。本研究针对基于布朗运动的DFM提供了精细化且新颖的收敛保证，重点分析了离散化误差。我们的分析基于Kullback-Leibler（KL）散度和2-Wasserstein距离展开。在有限矩条件和温和的分数可积性假设下，我们推导出KL收敛界，其维度依赖性优于先前工作，据我们所知，在最小条件下实现了当前最优的缩放性能。我们进一步将分析扩展到2-Wasserstein距离：在额外的一阶分数可积性假设和弱对数凹性条件下，我们获得了与KL情形一致的维度依赖性的收敛保证。