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 this https URL

本研究从数值角度考察了 DDIM 的机制，发现在解决相关的随机微分方程时可以利用一些特定的得分逼近，提出了一种解释 DDIM 加速效果的方法，并在此基础上对其进行了扩展以适用于一般扩散模型， coined 为 generalized DDIM (gDDIM)。在进行两种非各向同性扩散模型的验证时 (gDDIM) 得出了令人瞩目的加速效果。