While score-based diffusion models have achieved exceptional sampling quality, their sampling speeds are often limited by the high computational burden of score function evaluations. Despite the recent remarkable empirical advances in speeding up the score-based samplers, theoretical understanding of acceleration techniques remains largely limited. To bridge this gap, we propose a novel training-free acceleration scheme for stochastic samplers. Under minimal assumptions -- namely, $L^2$-accurate score estimates and a finite second-moment condition on the target distribution -- our accelerated sampler provably achieves $\varepsilon$-accuracy in total variation within $\widetilde{O}(d^{5/4}/\sqrt{\varepsilon})$ iterations, thereby significantly improving upon the $\widetilde{O}(d/\varepsilon)$ iteration complexity of standard score-based samplers. Notably, our convergence theory does not rely on restrictive assumptions on the target distribution or higher-order score estimation guarantees.

本研究解决了在高计算负担下，得分基扩散模型的采样速度受限的问题。提出了一种新颖的无训练加速方案，通过最小假设下的理论分析，证明加速采样器在总变差中以$\widetilde{O}(d^{5/4}/\sqrt{\varepsilon})$的迭代数达到了$\varepsilon$-精度，显著优于标准得分基采样器的$\widetilde{O}(d/\varepsilon)$复杂度。该理论不依赖于对目标分布的限制假设。 

在最小假设下的扩散模型可证加速