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：扩散模型在推理时存在样本生成速度慢的问题。尽管已有一些研究，但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。我们提出分裂积分器，用于在增广空间中对预训练扩散模型进行快速随机采样。分裂型积分器常用于分子动力学，它通过对涉及数据、辅助变量或噪声变量的数值更新进行巧妙交替，来提升采样效率。然而，我们发现直接应用分裂积分器在快速采样中并非最优。为此，我们针对原始分裂采样器提出若干有原则的改进措施以提升采样效率，并将改进后的采样器命名为简化分裂积分器。在CIFAR-10数据集上的相空间朗之万扩散（PSLD）[Pandey & Mandt, 2023]实验中，我们的随机采样器仅需100次网络函数评估（NFE）即可达到2.36的FID分数，而最优基线方法需2.63。