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.

本论文介绍了一种新的基于评分的生成模型（SGMs），通过利用均值场理论的概念来处理高基数数据分布。我们提出了均值场混沌扩散模型（MF-CDMs），通过利用相互作用粒子的混沌传播特性来解决高基数数据中固有的维度灾难问题。将高基数数据视为大型随机相互作用粒子系统，我们为无限维混沌粒子系统开发了一种新的分数匹配方法，并提出了一种有效的训练子分区策略的近似方案。我们的理论和实证结果证明了MF-CDMs在管理大型高基数数据结构（如3D点云）方面的可伸缩性和有效性。

均场混沌扩散模型