arXiv AI
Sep 25

FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference

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.

By Gatien S\'eguy (SATIE), Thomas Rodet (SATIE)
arXiv Statistics ML
Sep 30

Copula Active Subspaces I: A Score-Covariance Method for Reduced-Order Non-Gaussian Density Estimation

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.

By Joshua Chen, Peter Jan van Leeuwen