改进扩散模型的理论收敛性，提升维度依赖表现。
Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees
- 基于布朗运动的扩散流匹配新分析框架
- 在低矩条件下实现最优维度依赖的KL收敛界
- 首次在弱对数凹条件下给出2-Wasserstein保证
扩散流匹配（Diffusion Flow Matching, DFM）近期成为生成建模的通用框架，但其理论收敛性质仍不完整。本文针对基于布朗运动的DFM，聚焦离散化误差，从KL散度与2-Wasserstein距离两方面提供更精细的收敛保证。在有限阶矩与温和得分可积性假设下，推导出优于先前工作的维度依赖性KL收敛界，达到当前最优尺度。进一步地，在额外的一阶得分可积性与弱对数凹性条件下，获得与KL情形一致的2-Wasserstein收敛保证。
原文摘要 · Abstract (English)
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.
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