Local Flow Matching Generative Models

• URL: http://arxiv.org/abs/2410.02548v2
• Date: Tue, 31 Dec 2024 01:50:58 GMT
• Title: Local Flow Matching Generative Models
• Authors: Chen Xu, Xiuyuan Cheng, Yao Xie,
• Abstract summary: Local Flow Matching is a computational framework for density estimation based on flow-based generative models. $textttLFM$ employs a simulation-free scheme and incrementally learns a sequence of Flow Matching sub-models. We demonstrate the improved training efficiency and competitive generative performance of $textttLFM$ compared to FM.
• Score: 19.859984725284896
• License:
• Abstract: 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 ($\texttt{LFM}$), 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, $\texttt{LFM}$ 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 $\chi^2$-divergence between the generated and true data distributions. Experimentally, we demonstrate the improved training efficiency and competitive generative performance of $\texttt{LFM}$ 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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