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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.