🤖 AI Summary
To address the low sampling efficiency and sensitivity to noise estimation errors in Denoising Diffusion Probabilistic Models (DDPMs), this work proposes an error-robust implicit Adams numerical solver for diffusion ODEs. Methodologically, we design a dynamic Lagrange interpolation predictor grounded in noise-error modeling and introduce an adaptive error-suppression mechanism to enhance ODE solver stability. We pioneer the tight integration of the implicit Adams framework with diffusion ODE discretization. With only 10 network evaluations, our method achieves FID scores of 5.14, 9.42, and 9.69 on CIFAR-10, LSUN-Church, and LSUN-Bedroom, respectively—significantly outperforming same-step SOTA approaches. Our core contributions are threefold: (i) the first error-robust implicit Adams solving paradigm for diffusion models; (ii) an error-driven dynamic basis selection strategy; and (iii) simultaneous improvement in sampling quality and robustness under small step counts.
📝 Abstract
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.
