Mean-field Chaos Diffusion Models
This work addresses the curse of dimensionality in generative modeling for high-cardinality data, offering a novel approach that could benefit applications like 3D graphics, but it appears incremental as it builds on existing score-based generative models.
The paper tackles the problem of generating high-cardinality data distributions, such as 3D point clouds, by introducing mean-field chaos diffusion models (MF-CDMs), which leverage mean-field theory and interacting particles to address dimensionality issues, resulting in scalable and effective performance demonstrated through theoretical and empirical results.
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.