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）在生成任务上取得了显著成果，但其低采样效率仍限制了进一步应用。由于DDPMs可被形式化为扩散常微分方程（ODEs），许多快速采样方法可通过求解扩散ODEs推导得出。然而，我们发现以往具有固定分析形式的采样方法对预训练扩散模型估计的噪声中的误差缺乏鲁棒性。在本工作中，我们构建了一个误差鲁棒的Adams求解器（ERA-Solver），该求解器采用隐式Adams数值方法，包含预测器与校正器两个部分。不同于基于显式Adams方法的传统预测器，我们利用拉格朗日插值函数作为预测器，并通过误差鲁棒策略进一步增强，使其能够自适应选择估计噪声中误差更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，我们提出的ERA-Solver在仅需10次网络评估的情况下，分别实现了5.14、9.42和9.69的Fenchel Inception Distance（FID）图像生成指标。