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 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.