As diffusion probabilistic models (DPMs) are being employed as mainstream models for generative artificial intelligence (AI), the study of their memorization of the raw training data has attracted growing attention. Existing works in this direction aim to establish an understanding of whether or to what extent DPMs learn by memorization. Such an understanding is crucial for identifying potential risks of data leakage and copyright infringement in diffusion models and, more importantly, for more controllable generation and trustworthy application of Artificial Intelligence Generated Content (AIGC). While previous works have made important observations of when DPMs are prone to memorization, these findings are mostly empirical, and the developed data extraction methods only work for conditional diffusion models. In this work, we aim to establish a theoretical understanding of memorization in DPMs with 1) a memorization metric for theoretical analysis, 2) an analysis of conditional memorization with informative and random labels, and 3) two better evaluation metrics for measuring memorization. Based on the theoretical analysis, we further propose a novel data extraction method called \textbf{Surrogate condItional Data Extraction (SIDE)} that leverages a classifier trained on generated data as a surrogate condition to extract training data directly from unconditional diffusion models. Our empirical results demonstrate that SIDE can extract training data from diffusion models where previous methods fail, and it is on average over 50\% more effective across different scales of the CelebA dataset.

翻译：随着扩散概率模型（DPMs）成为生成式人工智能（AI）的主流模型，对其记忆原始训练数据的研究日益受到关注。该领域的现有工作旨在理解DPMs是否通过记忆学习，以及记忆的程度。这种理解对于识别扩散模型中数据泄露和版权侵权的潜在风险至关重要，更重要的是，对于实现人工智能生成内容（AIGC）的更可控生成和可信应用具有重要意义。尽管先前的工作对DPMs何时易于记忆做出了重要观察，但这些发现大多是经验性的，且已开发的数据提取方法仅适用于条件扩散模型。在本工作中，我们旨在建立对DPMs记忆的理论理解，包括：1）用于理论分析的记忆度量指标，2）对具有信息性标签和随机标签的条件记忆的分析，以及3）两种用于衡量记忆的更好评估指标。基于理论分析，我们进一步提出了一种名为\textbf{代理条件数据提取（SIDE）}的新数据提取方法，该方法利用在生成数据上训练的分类器作为代理条件，直接从无条件扩散模型中提取训练数据。我们的实证结果表明，SIDE能够从先前方法失败的扩散模型中提取训练数据，并且在CelebA数据集的不同规模上，其平均有效性提高了50%以上。