How Much Is Enough? A Study on Diffusion Times in Score-Based Generative Models

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, a detailed 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 with regard to the state of the art, according to standard sample quality metrics and log-likelihood.

Multi-Modal Latent Diffusion

“…In practice, we use a parametric score network s χ (r, t) to approximate the true score function, and we approximate q(r, T) with the stationary distribution ρ(r). Indeed, the generated data distribution q(r, 0) is close (in the KL sense) to the true density as described by [45,47]:…”