Mean-field Chaos Diffusion Models

TL;DR

This paper introduces mean-field chaos diffusion models, a new class of score-based generative models that effectively handle high-cardinality data by leveraging mean-field theory and chaos propagation, improving scalability and efficiency.

Contribution

The paper develops a novel score-matching method for infinite-dimensional chaotic particle systems and proposes an efficient subdivision training scheme for high-cardinality data.

Findings

Demonstrates scalability to large high-cardinality datasets

Shows effectiveness in modeling 3D point clouds

Validates theoretical properties through empirical results

Abstract

In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs), which address the curse of dimensionality inherent in high-cardinality data by utilizing the propagation of chaos property of interacting particles. By treating high-cardinality data as a large stochastic system of interacting particles, we develop a novel score-matching method for infinite-dimensional chaotic particle systems and propose an approximation scheme that employs a subdivision strategy for efficient training. Our theoretical and empirical results demonstrate the scalability and effectiveness of MF-CDMs for managing large high-cardinality data structures, such as 3D point clouds.