Towards a mathematical theory for consistency training in diffusion models
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929241164087296 |
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| author | Li, Gen Huang, Zhihan Wei, Yuting |
| author_facet | Li, Gen Huang, Zhihan Wei, Yuting |
| contents | Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into the training phase, consistency models attempt to train a sequence of consistency functions capable of mapping any point at any time step of the diffusion process to its starting point. Despite the empirical success, a comprehensive theoretical understanding of consistency training remains elusive. This paper takes a first step towards establishing theoretical underpinnings for consistency models. We demonstrate that, in order to generate samples within $\varepsilon$ proximity to the target in distribution (measured by some Wasserstein metric), it suffices for the number of steps in consistency learning to exceed the order of $d^{5/2}/\varepsilon$, with $d$ the data dimension. Our theory offers rigorous insights into the validity and efficacy of consistency models, illuminating their utility in downstream inference tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a mathematical theory for consistency training in diffusion models Li, Gen Huang, Zhihan Wei, Yuting Machine Learning Information Theory Statistics Theory Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into the training phase, consistency models attempt to train a sequence of consistency functions capable of mapping any point at any time step of the diffusion process to its starting point. Despite the empirical success, a comprehensive theoretical understanding of consistency training remains elusive. This paper takes a first step towards establishing theoretical underpinnings for consistency models. We demonstrate that, in order to generate samples within $\varepsilon$ proximity to the target in distribution (measured by some Wasserstein metric), it suffices for the number of steps in consistency learning to exceed the order of $d^{5/2}/\varepsilon$, with $d$ the data dimension. Our theory offers rigorous insights into the validity and efficacy of consistency models, illuminating their utility in downstream inference tasks. |
| title | Towards a mathematical theory for consistency training in diffusion models |
| topic | Machine Learning Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2402.07802 |