Understanding Diffusion Models by Feynman's Path Integral
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910370615001088 |
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| author | Hirono, Yuji Tanaka, Akinori Fukushima, Kenji |
| author_facet | Hirono, Yuji Tanaka, Akinori Fukushima, Kenji |
| contents | Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability flow ODEs) sampling schemes remain unclear. We introduce a novel formulation of diffusion models using Feynman's path integral, which is a formulation originally developed for quantum physics. We find this formulation providing comprehensive descriptions of score-based generative models, and demonstrate the derivation of backward stochastic differential equations and loss functions.The formulation accommodates an interpolating parameter connecting stochastic and deterministic sampling schemes, and we identify this parameter as a counterpart of Planck's constant in quantum physics. This analogy enables us to apply the Wentzel-Kramers-Brillouin (WKB) expansion, a well-established technique in quantum physics, for evaluating the negative log-likelihood to assess the performance disparity between stochastic and deterministic sampling schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11262 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Understanding Diffusion Models by Feynman's Path Integral Hirono, Yuji Tanaka, Akinori Fukushima, Kenji Machine Learning Statistical Mechanics Artificial Intelligence High Energy Physics - Theory Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability flow ODEs) sampling schemes remain unclear. We introduce a novel formulation of diffusion models using Feynman's path integral, which is a formulation originally developed for quantum physics. We find this formulation providing comprehensive descriptions of score-based generative models, and demonstrate the derivation of backward stochastic differential equations and loss functions.The formulation accommodates an interpolating parameter connecting stochastic and deterministic sampling schemes, and we identify this parameter as a counterpart of Planck's constant in quantum physics. This analogy enables us to apply the Wentzel-Kramers-Brillouin (WKB) expansion, a well-established technique in quantum physics, for evaluating the negative log-likelihood to assess the performance disparity between stochastic and deterministic sampling schemes. |
| title | Understanding Diffusion Models by Feynman's Path Integral |
| topic | Machine Learning Statistical Mechanics Artificial Intelligence High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.11262 |