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.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
PosteriorBench is a new benchmark that evaluates how well generative inverse solvers recover full posterior distributions rather than just a single reconstruction. It tests four physics-based inverse problems—Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference—using high-fidelity reference posteriors generated by rejection sampling and MCMC. The benchmark employs five metrics (posterior-mean error, posterior-standard-deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power-spectrum error) to assess pointwise accuracy, uncertainty, distributional alignment, and global frequency fidelity, revealing significant distribution-matching gaps in current solvers and highlighting the importance of neural operators, guidance weights, and generation noise for posterior-variance calibration.
arXiv:2609.12953v1 Announce Type: new Abstract: Flow matching approaches to imaging inverse problems commonly incorporate measurements in two ways. Conditioning-based approaches supply measurement-de...
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
The paper introduces flow matching as an amortized alternative to Markov chain Monte Carlo for sampling from posterior distributions in Bayesian inverse problems. By training a transport map on joint samples of parameters and data, the method produces independent approximate posterior samples for any observation at negligible online cost, eliminating the need for new likelihood evaluations. The authors provide accuracy estimates in total‑variation distance and Kullback‑Leibler divergence, propose a hybrid Metropolized sampler for exactness, and validate the approach on examples such as electrical impedance tomography and a likelihood‑free Lotka‑Volterra model.
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.
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.