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. All existing results have been obtained so far for time-homogeneous speed of the noise schedule. 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. Assuming that the score is Lipschitz continuous, we provide an improved error bound in Wasserstein distance, taking advantage of favourable underlying contraction mechanisms. We also propose an algorithm to automatically tune the noise schedule using the proposed upper bound. We illustrate empirically the performance of the noise schedule optimization in comparison to standard choices in the literature.

翻译：得分生成模型通过利用目标分布中添加噪声的样本学习得分函数，旨在估计目标数据分布。近期文献广泛聚焦于通过库尔贝克-莱布勒散度和沃瑟斯坦距离评估目标分布与估计分布之间的误差，进而衡量生成质量。现有研究结果均基于噪声调度的时间齐次速度。在数据分布的温和假设下，我们建立了目标分布与估计分布之间KL散度的上界，该上界显式依赖于任意时变噪声调度。假设得分函数满足Lipschitz连续性，我们利用有利的底层收缩机制，给出了沃瑟斯坦距离下改进的误差界。进一步，我们提出一种利用该上界自动调整噪声调度的算法。通过实验验证，我们展示了与文献中标准选择相比，噪声调度优化的性能优势。