Mean-field Chaos Diffusion Models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917688528338944 |
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| author | Park, Sungwoo Kim, Dongjun Alaa, Ahmed |
| author_facet | Park, Sungwoo Kim, Dongjun Alaa, Ahmed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean-field Chaos Diffusion Models Park, Sungwoo Kim, Dongjun Alaa, Ahmed Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition 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. |
| title | Mean-field Chaos Diffusion Models |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2406.05396 |