Convergence Of Consistency Model With Multistep Sampling Under General Data Assumptions
This work provides theoretical guarantees for consistency models, addressing the problem of slow sampling in diffusion models for researchers and practitioners in machine learning, though it is incremental as it builds on existing consistency model frameworks.
The paper tackles the computational expense of diffusion models by analyzing the convergence of consistency models under general data assumptions, showing that generated samples are close to the target distribution in Wasserstein or total variation distance with bounded support or smoothness conditions.
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from noise to data directly, which allows one-step fast data generation and multistep sampling to improve sample quality. In this paper, we study the convergence of consistency models when the self-consistency property holds approximately under the training distribution. Our analysis requires only mild data assumption and applies to a family of forward processes. When the target data distribution has bounded support or has tails that decay sufficiently fast, we show that the samples generated by the consistency model are close to the target distribution in Wasserstein distance; when the target distribution satisfies some smoothness assumption, we show that with an additional perturbation step for smoothing, the generated samples are close to the target distribution in total variation distance. We provide two case studies with commonly chosen forward processes to demonstrate the benefit of multistep sampling.