Diffusion probabilistic models (DPMs) are a powerful class of generative models known for their ability to generate high-fidelity image samples. A major challenge in the implementation of DPMs is the slow sampling process. In this work, we bring a high-efficiency sampler for DPMs. Specifically, we propose a score-based exact solution paradigm for the diffusion ODEs corresponding to the sampling process of DPMs, which introduces a new perspective on developing numerical algorithms for solving diffusion ODEs. To achieve an efficient sampler, we propose a recursive derivative estimation (RDE) method to reduce the estimation error. With our proposed solution paradigm and RDE method, we propose the score-integrand solver with the convergence order guarantee as efficient solver (SciRE-Solver) for solving diffusion ODEs. The SciRE-Solver attains state-of-the-art (SOTA) sampling performance with a limited number of score function evaluations (NFE) on both discrete-time and continuous-time DPMs in comparison to existing training-free sampling algorithms. Such as, we achieve $3.48$ FID with $12$ NFE and $2.42$ FID with $20$ NFE for continuous-time DPMs on CIFAR10, respectively. Different from other samplers, SciRE-Solver has the promising potential to surpass the FIDs achieved in the original papers of some pre-trained models with just fewer NFEs. For example, we reach SOTA value of $2.40$ FID with $100$ NFE for continuous-time DPM and of $3.15$ FID with $84$ NFE for discrete-time DPM on CIFAR-10, as well as of $2.17$ ($2.02$) FID with $18$ ($50$) NFE for discrete-time DPM on CelebA 64$\times$64.

翻译：扩散概率模型（DPMs）是一类强大的生成模型，以其生成高保真图像样本的能力而著称。DPMs实现中的主要挑战在于其缓慢的采样过程。本文提出了一种面向DPMs的高效采样器。具体而言，我们为对应DPMs采样过程的扩散常微分方程（ODE）提出了一种基于评分的精确解范式，为开发求解扩散ODE的数值算法提供了新视角。为实现高效采样器，我们提出了递归导数估计（RDE）方法来降低估计误差。基于所提出的解范式与RDE方法，我们设计了具有收敛阶保证的评分积分求解器（SciRE-Solver），用于高效求解扩散ODE。与现有无训练采样算法相比，SciRE-Solver在离散时间和连续时间DPMs上均能以有限评分函数评估次数（NFE）达到最先进的采样性能。例如，在CIFAR-10数据集上，对于连续时间DPMs，我们分别以12次NFE实现3.48的FID值，以20次NFE实现2.42的FID值。与其他采样器不同，SciRE-Solver具有仅需更少NFE即可超越部分预训练模型原始论文所获FID值的潜力。例如，在CIFAR-10数据集上，我们以100次NFE对连续时间DPM达到2.40的FID值，以84次NFE对离散时间DPM达到3.15的FID值；在CelebA 64×64数据集上，以18次（50次）NFE对离散时间DPM分别达到2.17（2.02）的FID值。