通过匹配流与发散度，显著提升生成模型精度
Improving Flow Matching by Aligning Flow Divergence
- 引入流与发散度联合优化的新目标函数
- 在动态系统、DNA序列和视频生成上性能提升明显
- 理论证明误差受流损失与发散损失共同约束
条件流匹配（CFM）是一种高效且无需模拟的生成模型训练方法，在数据生成任务中表现优异。然而，它难以保证概率路径学习的准确性。本文提出一种新的偏微分方程表征，刻画学习路径与真实路径之间的误差，并给出其解。我们证明，两条概率路径的总变差差距被CFM损失与相关发散损失的组合所上界控制。这一理论发现推动了新目标函数的设计，同时匹配流及其发散度。新方法在不牺牲生成效率的前提下，显著提升了流模型的性能。我们在动态系统、DNA序列和视频生成等重要基准任务上验证了该方法的优势。代码已公开于：https://github.com/Utah-Math-Data-Science/Flow_Div_Matching。
原文摘要 · Abstract (English)
Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in learning probability paths. In this paper, we introduce a new partial differential equation characterization for the error between the learned and exact probability paths, along with its solution. We show that the total variation gap between the two probability paths is bounded above by a combination of the CFM loss and an associated divergence loss. This theoretical insight leads to the design of a new objective function that simultaneously matches the flow and its divergence. Our new approach improves the performance of the flow-based generative model by a noticeable margin without sacrificing generation efficiency. We showcase the advantages of this enhanced training approach over CFM on several important benchmark tasks, including generative modeling for dynamical systems, DNA sequences, and videos. Code is available at \href{https://github.com/Utah-Math-Data-Science/Flow_Div_Matching}{Utah-Math-Data-Science}.
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