Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models

TL;DR

Analytic-DPM introduces an analytic, training-free method to estimate optimal reverse variance in diffusion models, significantly improving efficiency and sample quality by leveraging score functions and variance bounds.

Contribution

It provides the first analytic forms for optimal reverse variance and KL divergence in DPMs, enabling a fast, training-free inference framework with variance correction.

Findings

Improves log-likelihood of various DPMs

Produces high-quality samples

Achieves 20x to 80x speedup

Abstract

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.