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Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis — arXiv:2610.12052

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.12052
License (as archived): CC0-1.0
Archived: 2026-10-09T06:26:18.905Z
SHA-256 of the archived text: db1d5047e63a2d7d20849e570f8209229e243a31ff28469a901d9c92109fba7e
Stable URL of this page: https://metraipolis.com/documento/dc_69dbea7c19e5

How to cite

Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis — arXiv:2610.12052 — arXiv (en), https://arxiv.org/abs/2610.12052 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_69dbea7c19e5 (Metraipolis archive dc_69dbea7c19e5, sha256 db1d5047e63a2d7d20849e570f8209229e243a31ff28469a901d9c92109fba7e)

BibTeX

@misc{dc69dbea7c19e5,
  title = {Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis — arXiv:2610.12052},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.12052},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_69dbea7c19e5; sha256 db1d5047e63a2d7d20849e570f8209229e243a31ff28469a901d9c92109fba7e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.12052. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear. In this work, we leverage Gaussian distributions to isolate this phenomenon. We establish 2-Wasserstein convergence bounds for optimized hyperparameters, showing that diffusion processes achieve a sampling error of $O(\sqrt{d\lambda_{\max}}\log N/N)$, where $d$ is the dimension, $N$ the number of sampling steps, and $\lambda_{\max}$ the largest eigenvalue of the target covariance matrix. Unadjusted and underdamped Langevin dynamics suffer from an additional $\sqrt\kappa$ factor, where $\kappa$ is the condition number. These rates follow from spectral bounds which are sharp: we confirm them via matching first-order asymptotics as $N\rightarrow\infty$. Our analysis provides a rigorous characterization, in the Gaussian setting, of how time-dependent score trajectories remove condition-number dependence during sampling. By contrast, in the learning phase, we show that estimating the unnoised score by gradient descent leads to essentially the same estimator as estimating a noisy score, which suggests that the benefits of noising do not come from the learning phase.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.12052 — 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 2026-10-09T05:50:32.207Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).