An analysis of the noise schedule for score-based generative models
Abstract: 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.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: The main paper and appendices have been updated to address the primary concerns raised by the reviewers. Notably, we have added Appendix G to specifically address the concerns related to the case where the target distribution corresponds to real data.
Assigned Action Editor: ~Bruno_Loureiro1
Submission Number: 3425
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