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Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models — arXiv:2610.19042

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.19042
License (as archived): CC0-1.0
Archived: 2026-10-15T14:14:47.946Z
SHA-256 of the archived text: d98b58925b91fad4d99c40df54f022d52fc55b4cc754d60c6bf7f6d8d4cca992
Stable URL of this page: https://metraipolis.com/documento/dc_d65778badabe

How to cite

Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models — arXiv:2610.19042 — arXiv (en), https://arxiv.org/abs/2610.19042 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d65778badabe (Metraipolis archive dc_d65778badabe, sha256 d98b58925b91fad4d99c40df54f022d52fc55b4cc754d60c6bf7f6d8d4cca992)

BibTeX

@misc{dcd65778badabe,
  title = {Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models — arXiv:2610.19042},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.19042},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d65778badabe; sha256 d98b58925b91fad4d99c40df54f022d52fc55b4cc754d60c6bf7f6d8d4cca992},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.19042. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.19042 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T13:53:35.508Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).