Learning to Efficiently Sample from Diffusion Probabilistic Models

Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a powerful family of generative models that can yield high-fidelity samples and competitive log-likelihoods across a range of domains, including image and speech synthesis. Key advantages of DDPMs include ease of training, in contrast to generative adversarial networks, and speed of generation, in contrast to autoregressive models. However, DDPMs typically require hundreds-to-thousands of steps to generate a high fidelity sample, making them prohibitively expensive for high dimensional problems. Fortunately, DDPMs allow trading generation speed for sample quality through adjusting the number of refinement steps as a post process. Prior work has been successful in improving generation speed through handcrafting the time schedule by trial and error. We instead view the selection of the inference time schedules as an optimization problem, and introduce an exact dynamic programming algorithm that finds the optimal discrete time schedules for any pre-trained DDPM. Our method exploits the fact that ELBO can be decomposed into separate KL terms, and given any computation budget, discovers the time schedule that maximizes the training ELBO exactly. Our method is efficient, has no hyper-parameters of its own, and can be applied to any pre-trained DDPM with no retraining. We discover inference time schedules requiring as few as 32 refinement steps, while sacrificing less than 0.1 bits per dimension compared to the default 4,000 steps used on ImageNet 64x64 [Ho et al., 2020; Nichol and Dhariwal, 2021].