Mean-field Chaos Diffusion Models

Sungwoo Park, Dongjun Kim, Ahmed Alaa
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:39702-39736, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-park24f, title = {Mean-field Chaos Diffusion Models}, author = {Park, Sungwoo and Kim, Dongjun and Alaa, Ahmed}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {39702--39736}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/park24f/park24f.pdf}, url = {https://proceedings.mlr.press/v235/park24f.html}, 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.} }
Endnote
%0 Conference Paper %T Mean-field Chaos Diffusion Models %A Sungwoo Park %A Dongjun Kim %A Ahmed Alaa %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-park24f %I PMLR %P 39702--39736 %U https://proceedings.mlr.press/v235/park24f.html %V 235 %X 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.
APA
Park, S., Kim, D. & Alaa, A.. (2024). Mean-field Chaos Diffusion Models. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:39702-39736 Available from https://proceedings.mlr.press/v235/park24f.html.

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