ERA-Solver: Error-Robust Adams Solver for Fast Sampling of Diffusion Probabilistic Models

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 fast sampling methods with fixed analytical form are not able to robust with the various error patterns 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 errors in the estimated noise. The proposed solver can be directly applied to any pretrained diffusion models, without extra training. Experiments on Cifar10, CelebA, LSUN-Church, and ImageNet 64 x 64 (conditional) datasets demonstrate that our proposed ERA-Solver achieves 3.54, 5.06, 5.02, and 5.11 Frechet Inception Distance (FID) for image generation, with only 10 network evaluations.