  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.
