Score-based diffusion models, a recent framework for posterior sampling in Bayesian inverse problems, are applied to diffuse optical tomography (DOT), a highly ill‑posed boundary value problem for recovering tissue absorption and scattering. The authors introduce a mixed score that combines a learned component with a model‑based component, providing a theoretical justification for its local approximation to the true score in the small diffusion‑time regime. Four difference‑imaging approaches are compared—classical model‑based, approximate diffusion, exact posterior sampling (UCoS), and a regularized UCoS—showing that UCoS yields more accurate reconstructions, especially under limited‑view geometry and real experimental data.
By Fabian Schneider, Meghdoot Mozumder, Konstantin Tamarov, Leila Taghizadeh, Tanja Tarvainen, Tapio Helin, Duc-Lam Duong
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.
By Jiachen Yao, Zi-Siang Hsu, Xi Deng, Aditi Gupta, Xin Ju, Sally M Benson, Gege Wen, Anima Anandkumar
The paper introduces Scalable Bayesian Optimization of Composite Functions (SBOCF) for efficiently estimating physical parameters from scientific images, specifically targeting electron microscopy PACBED patterns. SBOCF leverages the composite structure of the image-matching objective, reducing modeled outputs from 24,649 to 11 by using patch-level summaries and correction terms. With only 50 simulator evaluations, SBOCF outperformed standard Bayesian optimization, achieving up to 290× lower median SSE on synthetic SrTiO3 benchmarks and producing accurate parameter estimates on experimental data without task-specific pretraining.
By Dasol Yoon, Poompol Buathong, Chia-Hao Lee, Yujia Zhang, David A. Muller, Peter I. Frazier
arXiv:2608. 09382v1 Announce Type: cross Abstract: Electromagnetic inverse scattering is a nonlinear and ill-posed problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging.
By Yutong Du, Zicheng Liu, Bo Qi, Yali Zong, Peixian Han
arXiv:2508. 05321v4 Announce Type: replace-cross Abstract: Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available.
By Laura Hellwege, Johann Christopher Engster, Moritz Schaar, Thorsten M. Buzug, Maik Stille
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 presents a method for training single‑step neural surrogates that can handle wave‑scattering inverse problems with tens of thousands of controllable variables. By dynamically generating training examples through gradient ascent and using a replay dataset with normalization, the authors achieve a surrogate that accurately models two‑dimensional wave scattering for up to 41,772 variables and can generalize to over 3 million variables without retraining. The surrogate demonstrates comparable or better performance than traditional FDTD simulations for large‑scale forward simulations and inverse design of photonic devices, achieving speedups up to 26.5×.
The paper presents a method for training single‑step neural surrogates that can handle wave‑scattering problems with tens of thousands of controllable variables. By dynamically generating training examples that highlight surrogate errors and using a replay dataset with normalization, the authors achieve a surrogate that accurately simulates two‑dimensional wave scattering for up to 41,772 variables and generalizes to over 3 million variables without retraining. The surrogate is applied to forward simulations and inverse design of freeform beam splitters and gradient‑index lenses, achieving speedups up to 26.5× compared to traditional FDTD methods.
By Charles Dove, Laura Waller
The paper introduces a coordinate-residual physics-driven neural network (CRPDNN) for 3‑D electromagnetic inverse scattering. CRPDNN models the unknown contrast distribution using normalized spatial coordinates and a residual convolutional network, optimizing parameters by enforcing consistency between measured and predicted scattered fields. It eliminates the need for preliminary reconstruction, achieving lower relative error and significant speedups compared to existing methods, while maintaining stability under noisy measurements and showing promise in practical imaging experiments.
By Yutong Du, Zicheng Liu, Bo Qi, Yali Zong, Peixian Han
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
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: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