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Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime — arXiv:2608.23938

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.23938
License (as archived): CC0-1.0
Archived: 2026-10-18T06:36:40.649Z
SHA-256 of the archived text: 168dccd2c8a6c8a6b19fb34c3f3f687bdad9f795d73ef78a4e923b8b54ba7d53
Stable URL of this page: https://metraipolis.com/documento/dc_efabacdff6ff

How to cite

Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime — arXiv:2608.23938 — arXiv (en), https://arxiv.org/abs/2608.23938 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_efabacdff6ff (Metraipolis archive dc_efabacdff6ff, sha256 168dccd2c8a6c8a6b19fb34c3f3f687bdad9f795d73ef78a4e923b8b54ba7d53)

BibTeX

@misc{dcefabacdff6ff,
  title = {Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime — arXiv:2608.23938},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.23938},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_efabacdff6ff; sha256 168dccd2c8a6c8a6b19fb34c3f3f687bdad9f795d73ef78a4e923b8b54ba7d53},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.23938. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Modern score-based generative models have achieved remarkable empirical success in high-dimensional tasks such as image, audio, and video synthesis. These models reduce distribution learning to a sequence of regression problems that, if solved exactly on finite data, would ultimately reproduce the training samples. Their ability to generalize must therefore arise from the implicit or explicit regularization during training. In this work, we develop a generative counterpart to the theory of benign overfitting and algorithmic regularization for overparameterized neural networks in the supervised lazy-training regime. We study denoising score matching in a vector-valued reproducing kernel Hilbert space with an inner-product kernel. In the proportional high-dimensional regime $n\asymp d$, we derive exact risk trajectories under gradient flow training. These trajectories exhibit three phases governed by qualitatively distinct estimators: a spectral estimator that generalizes, a pure-noise score with localized peaks that interpolate the training objective, and an empirical Bayes estimator that memorizes the data. We then analyze how these estimators combine along the reverse-time SDE and characterize the distribution of the resulting samples. The analysis reveals familiar mechanisms from supervised learning, including kernel linearization and self-induced regularization from the nonlinear part of the kernel, but also reveals a distinct phenomenology specific to generative modeling.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-26 in cs.LG).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG); Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2608.23938 — 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 2026-10-18T06:28:52.331Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-26?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).