How Much is Enough? A Study on Diffusion Times in Score-based Generative Models

TL;DR

This paper investigates the impact of diffusion time T in score-based generative models, proposing a method to optimize it for better quality and efficiency, supported by theoretical analysis and empirical results.

Contribution

It introduces a variational framework to analyze diffusion time T and proposes an auxiliary model to improve diffusion models with smaller T.

Findings

Smaller diffusion times can enhance training and sampling efficiency.

The auxiliary model effectively bridges the gap between ideal and actual diffusion dynamics.

Empirical results show competitive performance on image data.

Abstract

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.