Diffusion-based generative processes, formulated as differential equation solving, frequently balance computational speed with sample quality. Our theoretical investigation of ODE- and SDE-based solvers reveals complementary weaknesses: ODE solvers accumulate irreducible gradient error along deterministic trajectories, while SDE methods suffer from amplified discretization errors when the step budget is limited. Building upon this insight, we introduce AdaSDE, a novel single-step SDE solver that aims to unify the efficiency of ODEs with the error resilience of SDEs. Specifically, we introduce a single per-step learnable coefficient, estimated via lightweight distillation, which dynamically regulates the error correction strength to accelerate diffusion sampling. Notably, our framework can be integrated with existing solvers to enhance their capabilities. Extensive experiments demonstrate state-of-the-art performance: at 5 NFE, AdaSDE achieves FID scores of 4.18 on CIFAR-10, 8.05 on FFHQ and 6.96 on LSUN Bedroom. Codes are available in https://github.com/WLU-wry02/AdaSDE.

翻译：基于扩散的生成过程通常被表述为微分方程求解问题，其计算速度与样本质量之间常需权衡。我们对基于常微分方程（ODE）和随机微分方程（SDE）求解器的理论分析揭示了二者互补的缺陷：ODE求解器沿确定性轨迹会累积不可约的梯度误差，而SDE方法在步数预算有限时则受离散化误差放大的影响。基于这一洞察，我们提出了AdaSDE——一种新颖的单步SDE求解器，旨在将ODE的效率与SDE的误差鲁棒性相统一。具体而言，我们引入了一个可通过轻量级蒸馏估计的每步可学习系数，该系数动态调节误差校正强度以加速扩散采样。值得注意的是，我们的框架可与现有求解器集成以增强其性能。大量实验证明了其最先进的性能：在5次函数评估（NFE）条件下，AdaSDE在CIFAR-10上实现了4.18的FID分数，在FFHQ上为8.05，在LSUN Bedroom上为6.96。代码发布于https://github.com/WLU-wry02/AdaSDE。