Local Flow Matching Generative Models

2024-10-03

arXiv.org

AI Summary

This work addresses the challenge of density estimation by proposing Local Flow Matching (LFM), a novel framework that overcomes key limitations of conventional flow matching—namely, its reliance on numerical ODE solvers and high computational overhead. LFM constructs a continuous, normalized flow from noise to data via a cascade of small-step, invertible local reverse diffusion submodels, enabling simulation-free, progressive flow matching for the first time. Theoretically, we establish generation guarantees under the χ² divergence. Empirically, LFM significantly reduces model parameter count and training cost. On tabular and image generation benchmarks, it achieves competitive performance with standard flow matching while training substantially faster. Furthermore, LFM successfully generalizes to robot manipulation policy learning, demonstrating both broad applicability and practical utility.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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 ($ exttt{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, $ exttt{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 $ exttt{LFM}$ compared to FM on the unconditional generation of tabular data and image datasets and its applicability to robotic manipulation policy learning.

Problem

• Generative Models
• Machine Learning
• Data Simulation

Innovation

• Local Flow Matching
• Generative Modeling
• Accelerated Learning