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:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
By Yuchen Jiao, Na Li, Changxiao Cai, Yuxin Chen, Gen Li
The paper introduces a continuous normalizing flow model for infinite-dimensional Bayesian inference in inverse problems governed by partial differential equations. By defining a neural ordinary differential equation in an infinite-dimensional Hilbert space, a simple reference measure is transformed into a complex prior that captures prior information. The authors establish a theoretical framework for well-posedness, present training methods for two data settings, and provide sampling algorithms, applying the approach to smooth, scattering, and heat conduction inverse problems with supporting numerical experiments.
By Yang Zhao, Junxiong Jia, Tao Zhou
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:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
By Jing Jia, Wei Yuan, Sifan Liu, Liyue Shen, Guanyang Wang
The paper introduces LUD-DIF, a diffusion-based method that solves inverse problems using unpaired data. By deriving the evidence lower bound of the joint distribution and decoupling it into two independent diffusion processes under a weak‑coupling assumption, the authors provide a variational inference framework, a loss function, and an error‑bound analysis. Experiments show that LUD‑DIF performs well across multiple image inverse problems, demonstrating its effectiveness and generalization in unpaired settings.
By Chenglong Bao, Yiming Dang, Chenguang Duan, Yuling Jiao, Defeng Sun