  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.
