  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.
