为扩散流匹配模型提供可计算的KL散度上界，理论更扎实。
Theoretical guarantees in KL for Diffusion Flow Matching
- 基于布朗运动构造路径，通过学习漂移项实现生成
- 在分数分布有矩条件时，给出目标分布与生成分布间KL散度上界
- 适合关注生成模型理论保证的研究者阅读
流匹配（FM）是一类生成模型，旨在有限时间内通过固定耦合π和桥梁路径（确定或随机）将目标分布ν⋆与辅助分布μ连接。该路径定义了一个路径测度，可通过学习其马尔可夫投影的漂移项来近似。本文的主要贡献是在ν⋆、μ和π满足相对温和的假设下，对扩散流匹配（DFM）模型提供非渐近的理论保证，其中桥梁采用与布朗运动相关的条件分布。具体而言，在ν⋆、μ和π的分数具有矩条件，且满足标准的L²-漂移逼近误差假设的前提下，建立了目标分布与生成分布之间Kullback-Leibler（KL）散度的上界。
原文摘要 · Abstract (English)
Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows) stands out as a class of generative models that aims to bridge in finite time the target distribution $ν^\star$ with an auxiliary distribution $μ$, leveraging a fixed coupling $π$ and a bridge which can either be deterministic or stochastic. These two ingredients define a path measure which can then be approximated by learning the drift of its Markovian projection. The main contribution of this paper is to provide relatively mild assumptions on $ν^\star$, $μ$ and $π$ to obtain non-asymptotics guarantees for Diffusion Flow Matching (DFM) models using as bridge the conditional distribution associated with the Brownian motion. More precisely, we establish bounds on the Kullback-Leibler divergence between the target distribution and the one generated by such DFM models under moment conditions on the score of $ν^\star$, $μ$ and $π$, and a standard $L^2$-drift-approximation error assumption.
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