2024/02/07 by Stanislas Strasman, Antonio Ocello, Strasman, Stanislas +7 · 4 citations
Computer Science · Neuroscience · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Music Technology and Sound Studies #Music and Audio Processing #Neuroscience and Music Perception #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2402.04650
openalex publication_date 2024/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. Finally, we illustrate these bounds through numerical experiments using simulated and CIFAR-10 datasets, identifying an optimal range of noise schedules within a parametric family.