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.

翻译：基于分数的生成模型（SGMs）旨在仅利用目标分布经噪声扰动的样本来学习分数函数，从而估计目标数据分布。近期文献广泛关注于评估目标分布与估计分布之间的误差，通过Kullback-Leibler（KL）散度和Wasserstein距离来衡量生成质量。在对数据分布施加温和假设的条件下，我们建立了目标分布与估计分布之间KL散度的上界，该上界明确依赖于任意时间依赖的噪声调度。在附加的正则性假设下，利用有利的底层收缩机制，我们给出了相较于现有最优结果更紧的Wasserstein距离误差界。该上界不仅易于处理，而且同时包含了目标分布的特性与SGM训练过程中需调整的超参数。