  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.
