Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel

• URL: http://arxiv.org/abs/2406.00924v2
• Date: Thu, 17 Oct 2024 03:54:52 GMT
• Title: Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel
• Authors: Shivam Gupta, Linda Cai, Sitan Chen,
• Abstract summary: We show that our algorithm can be parallelized to run in only $widetilde O(log2 d)$ parallel rounds. We also show that our algorithm can be parallelized to run in only $widetilde O(log2 d)$ parallel rounds.
• Score: 10.840582511203024
• License:
• Abstract: Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works~\cite{chen2023sampling,chen2023ode,benton2023error,lee2022convergence} have proposed schemes for diffusion sampling with provable guarantees; these works show that for essentially any data distribution, one can approximately sample in polynomial time given a sufficiently accurate estimate of its score functions at different noise levels. In this work, we propose a new scheme inspired by Shen and Lee's randomized midpoint method for log-concave sampling~\cite{ShenL19}. We prove that this approach achieves the best known dimension dependence for sampling from arbitrary smooth distributions in total variation distance ($\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work). We also show that our algorithm can be parallelized to run in only $\widetilde O(\log^2 d)$ parallel rounds, constituting the first provable guarantees for parallel sampling with diffusion models. As a byproduct of our methods, for the well-studied problem of log-concave sampling in total variation distance, we give an algorithm and simple analysis achieving dimension dependence $\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work.

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