arXiv:2611.06979v1 Announce Type: new Abstract: M/EEG source imaging requires accurate localization and reliable uncertainty estimates, yet posterior credible regions are rarely assessed for empirica...
arXiv:2606. 17048v1 Announce Type: new Abstract: Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption.
arXiv:2507. 07008v2 Announce Type: replace Abstract: Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature.
arXiv:2603. 00393v2 Announce Type: replace-cross Abstract: Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy, incomplete data or inherent non-uniqueness.
FB‑GDM is a fully‑Bayesian guided diffusion method that eliminates the need for task‑specific hyperparameter tuning in linear inverse problems. It derives a closed‑form conditional score from a Gaussian approximation of ΦGDM, treating two precision parameters as latent variables inferred via variational inference at each reverse step. Experiments on CelebA‑HQ show that FB‑GDM outperforms ΦGDM at its nominal setting, matches a ground‑truth‑calibrated oracle within 0.1 dB, and remains robust to changes in the forward operator, noise level, or image distribution without hallucinations.
arXiv:2609. 36142v1 Announce Type: cross Abstract: In Bayesian inference problems with non-Gaussian observation noise, the posterior is only as accurate as the noise density, and gradient-based samplers need that density and its gradient evaluable pointwise, whether from an explicit expression or from code, and without an inner solve.
The paper introduces a spectral framework that decomposes the posterior covariance in sparse Bayesian learning for M/EEG source imaging into data‑informed and indeterminacy epistemic components, using the singular value structure of the prior‑preconditioned forward operator. It also presents an equivalent subtractive decomposition that expresses the prior covariance as the sum of posterior and data‑driven reduction terms, allowing precise accounting of uncertainty reduction through Bayesian learning. These complementary representations provide both theoretical insight and practical tools for interpretable uncertainty quantification in linear‑Gaussian Bayesian inverse solvers where the posterior covariance is available in closed form.
arXiv:2602. 11711v2 Announce Type: replace-cross Abstract: This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems.
arXiv:2606. 05381v1 Announce Type: new Abstract: We propose an extended family of structured spatial priors that incorporates the total variation (TV) function with $\ell_p$ norms.
arXiv:2610. 09281v1 Announce Type: new Abstract: In Bayesian inverse problems, posterior sampling requires generating samples that are consistent with given observations while capturing the range of plausible solutions.
arXiv:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
arXiv:2608. 01547v1 Announce Type: cross Abstract: Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations.