用随机龙格-库塔法加速扩散模型采样，理论证明更高效
Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models
- 基于随机龙格-库塔方法设计无训练加速采样器
- 理论误差达ε²，评估次数为O~(d^{3/2}/ε)
- 适合追求高效生成的模型研究者参考
扩散模型在现代生成建模中占据核心地位，在多个领域表现卓越。尽管生成样本质量高，主流基于SDE的采样器如DDPM通常需大量得分函数评估，计算成本远高于单步生成器（如GAN）。尽管已有多种加速方法，但其理论基础仍不充分。本文提出并分析了一种无需训练的SDE类扩散采样加速算法，基于随机龙格-库塔方法。该采样器在KL散度下可实现ε²的误差，仅需𝑛(d^{3/2}/ε)次得分函数评估（ε足够小时），在维度依赖性上优于现有最优结果𝑛(d^3/ε)。数值实验验证了方法的有效性。
原文摘要 · Abstract (English)
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.
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