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.

翻译：流匹配是一种无模拟方法，用于学习连续可逆流以插值两个分布，特别是在生成建模中实现从噪声生成数据。本文提出局部流匹配方法，该方法学习一系列流匹配子模型，每个子模型在数据到噪声方向上匹配步长时间内的扩散过程。在每一步中，子模型插值的两个分布比数据与噪声更接近，这使得可以使用更小的模型实现更快的训练。局部流匹配的逐步结构天然适合蒸馏，可采用不同的蒸馏技术加速生成。理论上，我们证明了所提流模型在生成分布与真实数据分布之间的$\chi^2$散度方面具有生成保证。实验中，我们在表格数据与图像数据集的无条件生成以及机器人操作策略的条件生成任务上，验证了局部流匹配相比流匹配具有更高的训练效率和具有竞争力的生成性能。