Diffusion models play a pivotal role in contemporary generative modeling, claiming state-of-the-art performance across various domains. Despite their superior sample quality, mainstream diffusion-based stochastic samplers like DDPM often require a large number of score function evaluations, incurring considerably higher computational cost compared to single-step generators like generative adversarial networks. While several acceleration methods have been proposed in practice, the theoretical foundations for accelerating diffusion models remain underexplored. In this paper, we propose and analyze a training-free acceleration algorithm for SDE-style diffusion samplers, based on the stochastic Runge-Kutta method. The proposed sampler provably attains $\varepsilon^2$ error -- measured in KL divergence -- using $\widetilde O(d^{3/2} / \varepsilon)$ score function evaluations (for sufficiently small $\varepsilon$), strengthening the state-of-the-art guarantees $\widetilde O(d^{3} / \varepsilon)$ in terms of dimensional dependency. Numerical experiments validate the efficiency of the proposed method.

翻译：扩散模型在当代生成建模中发挥着关键作用，在多个领域均展现出最先进的性能。尽管其样本质量优异，但以DDPM为代表的主流基于扩散的随机采样器通常需要大量评分函数评估，与生成对抗网络等单步生成器相比，计算成本显著更高。虽然实践中已提出多种加速方法，但加速扩散模型的理论基础仍未得到充分探索。本文基于随机Runge-Kutta方法，提出并分析了一种免训练的SDE风格扩散采样器加速算法。所提出的采样器在KL散度度量下可证明达到$\varepsilon^2$误差，仅需$\widetilde O(d^{3/2} / \varepsilon)$次评分函数评估（对于足够小的$\varepsilon$），在维度依赖性方面强化了现有最优保证$\widetilde O(d^{3} / \varepsilon)$。数值实验验证了该方法的有效性。