In recent years, there has been a surge of interest in proving discretization
bounds for diffusion models. 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 discretization scheme for diffusion
models 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.

近年来，在扩散模型的离散化界限方面出现了浓厚的兴趣，本文提出了一种新的受 Shen 和 Lee 随机中点方法启发的扩散模型离散化方案，证明了该方法在从任意平滑分布中进行采样的维度依赖方面达到了已知最佳结果，同时还展示了可以将算法并行化以实现更快速的采样。