Papers › Local Flow Matching Generative Models
Local Flow Matching Generative Models
Chen Xu, Xiuyuan Cheng, Yao Xie
Density estimation is a fundamental problem in statistics and machine learning. We consider a modern approach using flow-based generative models, and propose Local Flow Matching (LFM), a computational framework for density estimation based on such models, which learn a continuous and invertible flow to map noise samples to data samples. Unlike existing methods, LFM employs a simulation-free scheme and incrementally learns a sequence of Flow Matching sub-models. Each sub-model matches a diffusion process over a small step size in the data-to-noise direction. This iterative process reduces the gap between the two distributions interpolated by the sub-models, enabling smaller models with faster training times. Theoretically, we prove a generation guarantee of the proposed flow model regarding the χ²-divergence between the generated and true data distributions. Experimentally, 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 its applicability to robotic manipulation policy learning.
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