arXiv:2605. 15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends.
arXiv:2607. 08757v1 Announce Type: cross Abstract: Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory.
Diffusion posterior samplers reconstruct signals by combining a pretrained diffusion prior with a measurement likelihood specified by a forward model and a noise model. Calibration and reference data...
arXiv:2610.29102v1 Announce Type: new Abstract: Diffusion posterior samplers reconstruct signals by combining a pretrained diffusion prior with a measurement likelihood specified by a forward model a...
arXiv:2610. 12052v1 Announce Type: cross Abstract: Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear.
The paper demonstrates that diffusion models encode memorization in the geometry of their learned energy landscape before it becomes visible in generated samples. By analyzing score divergence and basin volume, the authors show that localized basins form around training images early in training, and that cyclic denoising can recover these images even when one‑shot generation shows no copies. Experiments on Gaussian mixtures, CelebA, CIFAR‑10, and Stable Diffusion v1.4 confirm that basin geometry reveals memorization across various settings.
arXiv:2609.35947v1 Announce Type: new Abstract: Many inference-time tasks for pretrained discrete diffusion models and diffusion language models reduce to drawing samples from a tilted version of the...
arXiv:2607. 08041v1 Announce Type: new Abstract: How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery.
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
arXiv:2606. 06179v1 Announce Type: cross Abstract: Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions.
arXiv:2609. 01166v1 Announce Type: cross Abstract: The present research is devoted to the nonparametric estimation of a density-dependent drift coefficient in a multivariate McKean--Vlasov diffusion from independent observations at a common time, as well as the stationary density.
How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery. To address this, we introduce analytically tractable Bayesian information restricted diffusion (BIRD) models, in which each pixel observes restricted information about noisy data.