Towards a mathematical theory for consistency training in diffusion models
<|reference_start|>Towards a mathematical theory for consistency training in diffusion models: 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.<|reference_end|>
@article{li2024towards,
    title={Towards a mathematical theory for consistency training in diffusion
  models},
    author={Gen Li, Zhihan Huang, Yuting Wei},
    journal={arXiv preprint arXiv:2402.07802},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.07802},
    primaryClass={stat.ML cs.IT cs.LG math.IT math.ST stat.TH}
}