Though denoising diffusion probabilistic models (DDPMs) have achieved remarkable generation results, the low sampling efficiency of DDPMs still limits further applications. Since DDPMs can be formulated as diffusion ordinary differential equations (ODEs), various fast sampling methods can be derived from solving diffusion ODEs. However, we notice that previous sampling methods with fixed analytical form are not robust with the error in the noise estimated from pretrained diffusion models. In this work, we construct an error-robust Adams solver (ERA-Solver), which utilizes the implicit Adams numerical method that consists of a predictor and a corrector. Different from the traditional predictor based on explicit Adams methods, we leverage a Lagrange interpolation function as the predictor, which is further enhanced with an error-robust strategy to adaptively select the Lagrange bases with lower error in the estimated noise. Experiments on Cifar10, LSUN-Church, and LSUN-Bedroom datasets demonstrate that our proposed ERA-Solver achieves 5.14, 9.42, and 9.69 Fenchel Inception Distance (FID) for image generation, with only 10 network evaluations.

翻译：尽管去噪扩散概率模型（DDPMs）在生成任务中取得了显著成果，但其低采样效率仍制约了进一步应用。由于DDPMs可被建模为扩散常微分方程（ODEs），通过求解扩散ODEs可推导出多种快速采样方法。然而，我们注意到以往具有固定解析形式的采样方法对预训练扩散模型估计噪声中的误差缺乏鲁棒性。本研究构建了误差鲁棒Adams求解器（ERA-Solver），该求解器采用由预测器与校正器组成的隐式Adams数值方法。与基于显式Adams方法的传统预测器不同，我们利用拉格朗日插值函数作为预测器，并进一步通过误差鲁棒策略增强其性能：自适应选取估计噪声中误差较低的拉格朗日基函数。在Cifar10、LSUN-Church和LSUN-Bedroom数据集上的实验表明，所提出的ERA-Solver仅需10次网络评估即可在图像生成任务中分别达到5.14、9.42和9.69的Fenchel Inception Distance（FID）指标。