arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
By Zilan Cheng, Li-Lian Wang, Zhongjian Wang
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.
By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
arXiv:2606. 20417v1 Announce Type: new Abstract: Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations.
By Christian Jimenez-Beltran, Aretha L. Teckentrup, Antonio Vergari, Konstantinos C. Zygalakis
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
By Yuanzhe Wang, Alexandre M. Tartakovsky
The paper introduces the Ensemble-conditioned Inverse Problem (EIP), a multivariate statistical framework for inferring an ensemble that follows the pushforward of a prior through a forward process. It applies to fields such as high‑energy physics, full waveform inversion, and inverse imaging, and proposes non‑iterative inference‑time methods using ensemble inverse generative models that avoid explicit forward model use during inference. The authors demonstrate the approach on synthetic and real datasets and provide code for replication.
By Zhengyan Huan, Camila Pazos, Martin Klassen, Vincent Croft, Pierre-Hugues Beauchemin, Shuchin Aeron
arXiv:2606. 17048v1 Announce Type: new Abstract: Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption.
By Abbas Mammadov, Ozgur Kara, Kaan Oktay, Iskander Azangulov, Adil Kaan Akan, Hyungjin Chung, James Matthew Rehg, Yee Whye Teh