Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models
This work addresses inference efficiency for users of diffusion models, offering a significant speed improvement while maintaining or enhancing performance, though it is incremental as it builds on existing score-based models.
The paper tackles the problem of expensive inference in diffusion probabilistic models by analytically deriving the optimal reverse variance and KL divergence, leading to Analytic-DPM, a training-free framework that improves log-likelihood, produces high-quality samples, and achieves a 20x to 80x speedup.
Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference is to estimate the variance in each timestep of the reverse process. In this work, we present a surprising result that both the optimal reverse variance and the corresponding optimal KL divergence of a DPM have analytic forms w.r.t. its score function. Building upon it, we propose Analytic-DPM, a training-free inference framework that estimates the analytic forms of the variance and KL divergence using the Monte Carlo method and a pretrained score-based model. Further, to correct the potential bias caused by the score-based model, we derive both lower and upper bounds of the optimal variance and clip the estimate for a better result. Empirically, our analytic-DPM improves the log-likelihood of various DPMs, produces high-quality samples, and meanwhile enjoys a 20x to 80x speed up.