Diffusion models suffer from slow sample generation at inference time. Despite recent efforts, improving the sampling efficiency of stochastic samplers for diffusion models remains a promising direction. We propose Splitting Integrators for fast stochastic sampling in pre-trained diffusion models in augmented spaces. Commonly used in molecular dynamics, splitting-based integrators attempt to improve sampling efficiency by cleverly alternating between numerical updates involving the data, auxiliary, or noise variables. However, we show that a naive application of splitting integrators is sub-optimal for fast sampling. Consequently, we propose several principled modifications to naive splitting samplers for improving sampling efficiency and denote the resulting samplers as Reduced Splitting Integrators. In the context of Phase Space Langevin Diffusion (PSLD) [Pandey \& Mandt, 2023] on CIFAR-10, our stochastic sampler achieves an FID score of 2.36 in only 100 network function evaluations (NFE) as compared to 2.63 for the best baselines.

翻译：扩散模型在推断时存在样本生成速度慢的问题。尽管已有相关工作，提升扩散模型随机采样器的采样效率仍是一个有前景的方向。本文提出在增强空间中针对预训练扩散模型使用分裂积分器实现快速随机采样。分裂积分器常用于分子动力学领域，通过巧妙地交替更新涉及数据、辅助变量或噪声变量的数值计算，旨在提升采样效率。然而，我们证明直接应用分裂积分器在快速采样方面并非最优。为此，我们针对原始分裂采样器提出多项原则性改进以提升采样效率，并将改进后的采样器称为约化分裂积分器。在CIFAR-10数据集上的相空间朗之万扩散（PSLD）[Pandey & Mandt, 2023]框架下，我们的随机采样器仅需100次网络函数评估即可达到2.36的FID评分，而最优基线方法的评分为2.63。