Towards a mathematical theory for consistency training in diffusion
models
- URL: http://arxiv.org/abs/2402.07802v1
- Date: Mon, 12 Feb 2024 17:07:02 GMT
- Title: Towards a mathematical theory for consistency training in diffusion
models
- Authors: Gen Li, Zhihan Huang, Yuting Wei
- Abstract summary: 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, it suffices for the number of steps in consistency learning to exceed the order of $d5/2/varepsilon$, with the data dimension.
Our theory offers rigorous insights into the validity and efficacy of consistency models, illuminating their utility in downstream inference tasks.
- Score: 17.632123036281957
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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