用p-Laplace分析识别扩散模型记忆的训练数据，无需原始文本即可检测。
Identifying Memorization of Diffusion Models through $p$-Laplace Analysis: Estimators, Bounds and Applications
- 通过学习到的得分函数构造p-Laplace近似，探测概率景观中的高阶差异。
- 在500个记忆提示（约3000张图）上验证，可有效识别生成后的记忆内容。
- 首次在文生图模型中应用该方法，特别适合条件文本缺失场景。
扩散模型作为当前主流图像生成模型，通过估计扰动数据样本的对数概率梯度（即得分函数）来建模分布，而无需直接访问真实概率分布。本文研究是否可利用该估计得分函数计算高阶微分——p-Laplace算子。结果表明，这些算子可用于识别模型中记忆的训练数据。我们提出一种基于学习得分函数的数值p-Laplace近似方法，展示了其在揭示概率景观关键特征方面的有效性。同时，理论证明了估计器的误差界，并通过数值实验加以验证。在高斯混合模型结构化案例中分析后，进一步将结果推广至文生图模型（text-to-image），首次实现基于p-Laplace算子的记忆识别，在500个记忆提示（约3000张生成图像）的后生成阶段表现出显著优势，尤其在条件文本不可用时仍具鲁棒性。
原文摘要 · Abstract (English)
Diffusion models, today's leading image generative models, estimate the score function, i.e. the gradient of the log probability of (perturbed) data samples, without direct access to the underlying probability distribution. This work investigates whether the estimated score function can be leveraged to compute higher-order differentials, namely the p-Laplace operators. We show that these operators can be employed to identify memorized training data. We propose a numerical p-Laplace approximation based on the learned score functions, showing its effectiveness in identifying key features of the probability landscape. Furthermore, theoretical error-bounds to these estimators are proven and demonstrated numerically. We analyze the structured case of Gaussian mixture models, and demonstrate that the results carry-over to text-conditioned image generative models (text-to-image), where memorization identification based on the p-Laplace operator is performed for the first time, showing its advantage on 500 memorized prompts ($\sim$3000 generated images) in a post-generation regime, especially when the conditioning text is unavailable.
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