  The past few years have witnessed the great success of Diffusion models~(DMs)
in generating high-fidelity samples in generative modeling tasks. A major
limitation of the DM is its notoriously slow sampling procedure which normally
requires hundreds to thousands of time discretization steps of the learned
diffusion process to reach the desired accuracy. Our goal is to develop a fast
sampling method for DMs with a much less number of steps while retaining high
sample quality. To this end, we systematically analyze the sampling procedure
in DMs and identify key factors that affect the sample quality, among which the
method of discretization is most crucial. By carefully examining the learned
diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS).
It is based on the Exponential Integrator designed for discretizing ordinary
differential equations (ODEs) and leverages a semilinear structure of the
learned diffusion process to reduce the discretization error. The proposed
method can be applied to any DMs and can generate high-fidelity samples in as
few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU
to generate $50k$ images from CIFAR10. Moreover, by directly using pre-trained
DMs, we achieve the state-of-art sampling performance when the number of score
function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID,
and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at
https://github.com/qsh-zh/deis
