gDDIM: Generalized denoising diffusion implicit models
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Our goal is to extend the denoising diffusion implicit model (DDIM) to general diffusion models (DMs). Instead of constructing a non-Markov noising process as in the original DDIM paper, 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 with a small but delicate modification in parameterizing the score network. When applied to the critically-damped Langevin diffusion model, a new type of diffusion model proposed recently by augmenting the diffusion process with velocity, our algorithm achieves an FID score of 2.28, on CIFAR10, with only 50 number of score function evaluations (NFEs) and an FID score of 2.87 with only 27 NFEs, better than all existing methods with the same NFEs. Code is available at https://github.com/qsh-zh/gDDIM
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