  Our goal is to extend the denoising diffusion implicit model (DDIM) to
general diffusion models~(DMs) besides isotropic diffusions. Instead of
constructing a non-Markov noising process as in the original DDIM, we examine
the mechanism of DDIM from a numerical perspective. We discover that the DDIM
can be obtained by using some specific approximations of the score when solving
the corresponding stochastic differential equation. We present an
interpretation of the accelerating effects of DDIM that also explains the
advantages of a deterministic sampling scheme over the stochastic one for fast
sampling. Building on this insight, we extend DDIM to general DMs, coined
generalized DDIM (gDDIM), with a small but delicate modification in
parameterizing the score network. We validate gDDIM in two non-isotropic DMs:
Blurring diffusion model (BDM) and Critically-damped Langevin diffusion model
(CLD). We observe more than 20 times acceleration in BDM. In the CLD, a
diffusion model by augmenting the diffusion process with velocity, our
algorithm achieves an FID score of 2.26, on CIFAR10, with only 50 number of
score function evaluations~(NFEs) and an FID score of 2.86 with only 27 NFEs.
Code is available at https://github.com/qsh-zh/gDDIM
