An analysis of the noise schedule for score-based generative models

Stanislas Strasman (1, 2) , Antonio Ocello (3) , Claire Boyer (2, 4) , Sylvain Le Corff (2, 1) , Vincent Lemaire (2)

1 SU - Sorbonne Université
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique
4 IUF - Institut universitaire de France

Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target. Recent literature has focused extensively on assessing the error between the target and estimated distributions, gauging the generative quality through the Kullback-Leibler (KL) divergence and Wasserstein distances. Under mild assumptions on the data distribution, we establish an upper bound for the KL divergence between the target and the estimated distributions, explicitly depending on any time-dependent noise schedule. Under additional regularity assumptions, taking advantage of favorable underlying contraction mechanisms, we provide a tighter error bound in Wasserstein distance compared to state-of-the-art results. In addition to being tractable, this upper bound jointly incorporates properties of the target distribution and SGM hyperparameters that need to be tuned during training.

Keywords: Score-based generative models; Diffusion models; Noise schedule; Wasserstein distance; Kullback Leibler Divergence

Domains: Machine Learning [stat.ML]; Statistics [math.ST]

Stanislas Strasman, Antonio Ocello, Claire Boyer, Sylvain Le Corff, Vincent Lemaire. An analysis of the noise schedule for score-based generative models. 2024. ⟨hal-04441680v3⟩