Flow Matching (FM) is a simulation-free method for learning a continuous and invertible flow to interpolate between two distributions, and in particular to generate data from noise in generative modeling. In this paper, we introduce Local Flow Matching (LFM), which learns a sequence of FM sub-models and each matches a diffusion process up to the time of the step size in the data-to-noise direction. In each step, the two distributions to be interpolated by the sub-model are closer to each other than data vs. noise, and this enables the use of smaller models with faster training. The stepwise structure of LFM is natural to be distilled and different distillation techniques can be adopted to speed up generation. Theoretically, we prove a generation guarantee of the proposed flow model in terms of the $\chi^2$-divergence between the generated and true data distributions. In experiments, we demonstrate the improved training efficiency and competitive generative performance of LFM compared to FM on the unconditional generation of tabular data and image datasets, and also on the conditional generation of robotic manipulation policies.

本研究针对现有流匹配方法在生成建模中的效率问题，提出了一种局部流匹配（LFM）的方法，通过学习一系列流匹配子模型，以适应数据到噪声的扩散过程。结果表明，与传统方法相比，LFM在训练效率和生成性能上有显著提升，特别是在无条件生成表格数据和图像数据集方面。

局部流匹配生成模型