gDDIM: Generalized denoising diffusion implicit models

TL;DR

This paper extends DDIM to general diffusion models, providing a theoretical understanding and demonstrating significant acceleration and improved sampling efficiency in non-isotropic diffusion models like BDM and CLD.

Contribution

The paper introduces gDDIM, a novel extension of DDIM for general diffusion models, with a new score parameterization and theoretical insights into acceleration mechanisms.

Findings

Over 20x acceleration in BDM.

Achieved FID of 2.26 with 50 NFEs on CIFAR10.

Achieved FID of 2.86 with 27 NFEs on CIFAR10.

Abstract

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