arXiv：cs.LG· Marta Gentiloni Silveri, Giovanni Conforti, Alain Durmus·· 5 小时前AI 评分33
Diffusion Flow Matching 的维度改进 KL 界与 Wasserstein 保证
Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees
AI 导读
研究为基于布朗运动的 Diffusion Flow Matching（DFM）给出更精细的收敛保证，聚焦离散化误差，在 KL 散度与 2-Wasserstein 距离下分析。
正文
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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.16610 [stat.ML] |
| (or arXiv:2606.16610v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2606.16610 arXiv-issued DOI via DataCite |
Submission history
From: Marta Gentiloni Silveri [view email]
[v1]
Mon, 15 Jun 2026 12:00:13 UTC (68 KB)
[v2]
Fri, 2 Oct 2026 12:07:16 UTC (68 KB)
来源：arXiv：cs.LG · arxiv.org