Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose SA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that SA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art sampling methods for few-step sampling; 2) SOTA FID scores on substantial benchmark datasets under a suitable number of function evaluations (NFEs).

翻译：扩散概率模型（DPMs）已在生成任务中取得显著成功。由于从DPMs采样等价于求解耗时的扩散SDE或ODE，许多基于改进微分方程求解器的快速采样方法被提出。这类方法大多考虑求解扩散ODE，因其效率更优。然而，随机采样在生成多样且高质量数据方面可能具有额外优势。本文从方差控制扩散SDE和线性多步SDE求解器两个维度对随机采样进行全面分析。基于分析，我们提出SA-Solver——一种用于求解扩散SDE以生成高质量数据的改进高效随机Adams方法。实验表明，SA-Solver在少步采样中：1) 相较于现有最先进采样方法性能提升或相当；2) 在适宜的函数评估次数（NFEs）下，于多个基准数据集取得SOTA FID分数。