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。

基于随机中点的更快扩散采样：连续和并行

Faster Diffusion-based Sampling with Randomized Midpoints: Sequential  and Parallel

Diffusion models are powerful generative models but suffer from slow
sampling, often taking 1000 sequential denoising steps for one sample. As a
result, considerable efforts have been directed toward reducing the number of
denoising steps, but these methods hurt sample quality. Instead of reducing the
number of denoising steps (trading quality for speed), in this paper we explore
an orthogonal approach: can we run the denoising steps in parallel (trading
compute for speed)? In spite of the sequential nature of the denoising steps,
we show that surprisingly it is possible to parallelize sampling via Picard
iterations, by guessing the solution of future denoising steps and iteratively
refining until convergence. With this insight, we present ParaDiGMS, a novel
method to accelerate the sampling of pretrained diffusion models by denoising
multiple steps in parallel. ParaDiGMS is the first diffusion sampling method
that enables trading compute for speed and is even compatible with existing
fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we
improve sampling speed by 2-4x across a range of robotics and image generation
models, giving state-of-the-art sampling speeds of 0.2s on 100-step
DiffusionPolicy and 16s on 1000-step StableDiffusion-v2 with no measurable
degradation of task reward, FID score, or CLIP score.

本文介绍了一种新的方法 ParaDiGMS，通过并行执行多个去噪步骤来加速预训练扩散模型的采样速度。该方法通过使用 Picard 迭代猜测未来去噪步骤的解，并迭代地进行加工，从而使扩散采样过程可以并行化，使计算机可用性更高。使用 ParaDiGMS，各种机器人和图像生成模型的采样速度提高 2-4 倍，无论对任务奖励、FID 分数、还是 CLIP 分数都没有任何可感知的退化。