A Good Score Does not Lead to A Good Generative Model

• DOI: 10.48550/arxiv.2401.04856
• Publication Date: 2024-01-01
• Authors: Sixu Li; Shi Chen; Qin Li
• Keywords: Generative model; Argument (complex analysis); Sample (material); Kernel (algebra); Kernel density estimation

Score-based Generative Models (SGMs) is one leading method in generative modeling, renowned for their ability to generate high-quality samples from complex, high-dimensional data distributions. The enjoys empirical success and supported by rigorous theoretical convergence properties. In particular, it has been shown that SGMs can a distribution close the ground-truth if underlying score function learned well, suggesting of SGM as model. We provide counter-example this paper. Through sample complexity argument, we specific setting where well. Yet, only output are Gaussian blurring training points, mimicking effects kernel density estimation. finding resonates series recent reveal demonstrate strong memorization effect fail generate.