Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at \url{https://github.com/mandt-lab/PSLD}.

翻译：扩散模型在推理时存在样本生成速度慢的问题。因此，为更广泛的扩散模型构建一个原则性的框架以实现快速确定性/随机采样是一个有前景的研究方向。我们提出了两个互补的框架来加速预训练模型中的样本生成：共轭积分器和分裂积分器。共轭积分器推广了DDIM，将反向扩散动力学映射到一个更适合采样的空间。相比之下，分子动力学中常用的分裂积分器，通过巧妙地在涉及数据和辅助变量的数值更新之间交替，减少了数值模拟误差。在对这些方法进行广泛的实证和理论研究后，我们提出了一种混合方法，该方法在增广空间中实现了扩散模型中最佳的性能报告。应用于CIFAR-10上的相空间朗之万扩散[Pandey & Mandt, 2023]，我们的确定性采样器和随机采样器仅通过100次网络函数评估（NFE）就分别达到了2.11和2.36的FID分数，而最佳性能基线的对应分数分别为2.57和2.63。我们的代码和模型检查点将在\url{https://github.com/mandt-lab/PSLD}公开提供。