通过最优加速度传输改进流匹配，提升生成模型性能。
OAT-FM: Optimal Acceleration Transport for Improved Flow Matching
- 基于最优加速度传输理论，优化样本与速度的联合空间运输路径。
- 新方法在多个生成任务中稳定提升模型表现，无需大量噪声数据对。
- 提出两阶段微调范式，避免分布漂移，适合已有生成模型的增强。
流匹配（Flow Matching, FM）作为生成建模的强大技术，旨在从噪声到数据学习速度场，常被解释并实现为求解最优传输（OT）问题。本文将FM与近期最优加速度传输（OAT）理论相连接，提出改进的FM方法OAT-FM，并探索其理论与实践优势。我们证明，现有基于OT的FM方法隐含的直线化目标，数学上等价于最小化由OAT定义的物理作用量（对应加速度）。因此，OAT-FM不强制恒定速度，而是在样本与速度的乘积空间中优化加速度传输，其目标对应流直线化的充要条件。设计了高效算法以低复杂度实现OAT-FM。该方法启发了一种新的两阶段FM范式：给定一个任意FM方法训练出的生成模型，若其速度信息相对可靠，可通过OAT-FM进行微调以进一步提升性能。该范式消除了数据分布漂移风险，且无需生成大量噪声数据对，在多种生成任务中持续提升模型表现。代码已开源：https://github.com/AngxiaoYue/OAT-FM
原文摘要 · Abstract (English)
As a powerful technique in generative modeling, Flow Matching (FM) aims to learn velocity fields from noise to data, which is often explained and implemented as solving Optimal Transport (OT) problems. In this study, we bridge FM and the recent theory of Optimal Acceleration Transport (OAT), developing an improved FM method called OAT-FM and exploring its benefits in both theory and practice. In particular, we demonstrate that the straightening objective hidden in existing OT-based FM methods is mathematically equivalent to minimizing the physical action associated with acceleration defined by OAT. Accordingly, instead of enforcing constant velocity, OAT-FM optimizes the acceleration transport in the product space of sample and velocity, whose objective corresponds to a necessary and sufficient condition of flow straightness. An efficient algorithm is designed to achieve OAT-FM with low complexity. OAT-FM motivates a new two-phase FM paradigm: Given a generative model trained by an arbitrary FM method, whose velocity information has been relatively reliable, we can fine-tune and improve it via OAT-FM. This paradigm eliminates the risk of data distribution drift and the need to generate a large number of noise data pairs, which consistently improves model performance in various generative tasks. Code is available at: https://github.com/AngxiaoYue/OAT-FM
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