  Despite the remarkable success of diffusion models in image generation, slow
sampling remains a persistent issue. To accelerate the sampling process, prior
studies have reformulated diffusion sampling as an ODE/SDE and introduced
higher-order numerical methods. However, these methods often produce divergence
artifacts, especially with a low number of sampling steps, which limits the
achievable acceleration. In this paper, we investigate the potential causes of
these artifacts and suggest that the small stability regions of these methods
could be the principal cause. To address this issue, we propose two novel
techniques. The first technique involves the incorporation of Heavy Ball (HB)
momentum, a well-known technique for improving optimization, into existing
diffusion numerical methods to expand their stability regions. We also prove
that the resulting methods have first-order convergence. The second technique,
called Generalized Heavy Ball (GHVB), constructs a new high-order method that
offers a variable trade-off between accuracy and artifact suppression.
Experimental results show that our techniques are highly effective in reducing
artifacts and improving image quality, surpassing state-of-the-art diffusion
solvers on both pixel-based and latent-based diffusion models for low-step
sampling. Our research provides novel insights into the design of numerical
methods for future diffusion work.
