The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.
By Yixuan Sun, Anirban Samaddar, Sandeep Madireddy
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:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
By Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer, Andrew B. Duncan
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
arXiv:2610.19187v1 Announce Type: cross
Abstract: Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed,...
By Chao Li, Mrinal K. Sen, Sergey Fomel, Yangkang Chen
The paper introduces a structured posterior‑correction framework that blends a tractable Gaussian reference with data‑driven corrections learned via diffusion models. After applying mean correction and covariance calibration, the diffusion model focuses on a low‑dimensional subspace that captures discrepancies from the Gaussian reference, while the remaining space stays Gaussian. Experiments on three scientific inference tasks show that these corrections recover hidden modes, improve sample structure, and reduce prediction error compared to the Gaussian reference, with trade‑offs between accuracy and computational cost relative to full‑field generative models.
By Tobias Weber, Carla Sagebiel, Philipp Hennig
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:2603. 00205v2 Announce Type: replace-cross Abstract: Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems.
By Jiayang Shi, Lincen Yang, Zhong Li, Tristan van Leeuwen, Daniel M. Pelt, K. Joost Batenburg
arXiv:2609.15702v1 Announce Type: new
Abstract: Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is of...
By Zihao Wang
The paper introduces Energy‑Guided Transport, a training‑free framework that enforces nonlinear physical constraints in Flow Matching generative models by applying a continuous dissipative force derived from a smooth potential energy landscape. Unlike traditional rigid algebraic projections, this method steers intermediate generative states toward the physical manifold without interrupting ODE integration, preserving natural dynamics and achieving πO(N) complexity. Experiments on 1D and 2D systems, including chaotic Navier‑Stokes equations, demonstrate stable generation, improved stability‑accuracy trade‑offs, and faster inference compared to exact projection strategies.
By Giuliano Galadini, Aurelio Uncini, Danilo Comminiello
arXiv:2604. 01313v2 Announce Type: replace Abstract: High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation.
By Zeyu Xia, Tyler Kim, Trevor Reed, Judy Fox, Geoffrey Fox, Adam Szczepaniak
arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.
By Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai