In this paper, we introduce a geometric framework to analyze memorization in diffusion models using the eigenvalues of the Hessian of the log probability density. We propose that memorization arises from isolated points in the learned probability distribution, characterized by sharpness in the probability landscape, as indicated by large negative eigenvalues of the Hessian. Through experiments on various datasets, we demonstrate that these eigenvalues effectively detect and quantify memorization. Our approach provides a clear understanding of memorization in diffusion models and lays the groundwork for developing strategies to ensure secure and reliable generative models

翻译：本文提出一种几何框架，通过分析对数概率密度Hessian矩阵的特征值来研究扩散模型中的记忆化现象。我们认为记忆化源于学习概率分布中的孤立点，这些点通过概率景观的锐度（表现为Hessian矩阵的大幅负特征值）得以表征。通过在多个数据集上的实验，我们证明这些特征值能有效检测并量化记忆化程度。该方法为理解扩散模型的记忆化机制提供了清晰的理论视角，并为开发安全可靠的生成模型奠定了理论基础。