arXiv：cs.LG· Shashank Sule, Xinyue Yu, Boonam Shin, Yuxuan Liu, Abolfazl Hashemi, Hayden Schaeffer·· 2 小时前
损失曲率作为扩散模型记忆化的无采样代理指标
Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models
AI 导读
研究提出用输入损失曲率（扩散模型训练损失 Hessian 的 Frobenius 范数）量化扩散模型的记忆化。训练与验证样本的平均输入曲率可判断模型何时开始复述训练数据，但不足以衡量单个样本被记忆的概率。作者引入扩散模型的反事实记忆化定义，证明其由留一模型的输入曲率控制，建立样本局部损失景观与生成概率的理论联系。
正文
Abstract:Understanding the mechanism behind why diffusion models memorize their training data remains an open question in generative modeling. In this paper, we examine this question from two perspectives: (a) the model-level perspective concerning the onset of memorization in a model during training, and (b) the sample-level perspective concerning the proclivity of an individual sample to be memorized by a given model. We show that the so-called input loss curvature, or the Frobenius norm of the Hessian of the diffusion model's training loss, is an effective metric for quantifying both perspectives on memorization. In particular, we empirically demonstrate that input curvatures averaged across training and validation samples can identify when a model is likely to start regurgitating its training data when tracked over training time. However, this metric is not sufficient for measuring an individual sample's likelihood of being memorized. To address this perspective, we introduce a counterfactual definition of memorization in diffusion models, extending the analogous notion from supervised learning proposed by [Feldman, 2019]. We prove that this counterfactual memorization is controlled by the input curvature of the leave-one-out model, thus establishing a direct theoretical link between a sample's local loss landscape and its generation likelihood. We validate our derived bounds through several empirical experiments and show that input-dependent curvature provides a proxy for memorization.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.19042 [cs.LG] |
| (or arXiv:2610.19042v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.19042 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Xinyue Yu [view email]
[v1]
Tue, 13 Oct 2026 18:31:16 UTC (19,889 KB)
来源：arXiv：cs.LG · arxiv.org