Mean-field Chaos Diffusion Models
<|reference_start|>Mean-field Chaos Diffusion Models: 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.<|reference_end|>
@article{park2024mean-field,
    title={Mean-field Chaos Diffusion Models},
    author={Sungwoo Park, Dongjun Kim, Ahmed Alaa},
    journal={arXiv preprint arXiv:2406.05396},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05396},
    primaryClass={cs.LG cs.AI cs.CV}
}