Physical-State-Guided Diffusion Sampling (PSG) couples a persistent physical velocity model to a diffusion prior via a Gaussian bridge, allowing the physical state to be refined by waveform fitting while guiding the reverse diffusion process. This approach separates wave‑equation and denoiser gradients, preserving conventional FWI initialization and optimization history. PSG outperforms classical and diffusion‑based baselines on four OpenFWI families, maintains strong structural recovery under noise, and supports large‑scale models like Marmousi, Overthrust, and BP2004 Salt without retraining.
By Chen Min, Haowen Jiang, Zheng Ma, Xiongbin Yan
arXiv:2606. 14139v1 Announce Type: new Abstract: Full waveform inversion (FWI) recovers subsurface velocity from seismic recordings by solving a severely ill-posed, nonconvex PDE-constrained optimization.
By Chen Min, Zheng Ma
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 presents a seismic acoustic impedance inversion framework that uses a conditional latent generative diffusion model. By performing inversion in latent space and incorporating a lightweight wavelet-based module, the method reduces training overhead and improves efficiency. Numerical and field experiments show high accuracy, strong generalization, and enhanced geological detail with fewer diffusion steps.
By Jie Chen, Hongling Chen, Jinghuai Gao, Chuangji Meng, Tao Yang, XinXin Liang
arXiv:2603. 06829v2 Announce Type: replace Abstract: Subsurface ore detection is of paramount importance given the rising depletion of shallow mineral resources in recent years.
By Dhruman Gupta (Ashoka University), Yashas Shende (Ashoka University), Aritra Das (Ashoka University), Chanda Grover Kamra (Ashoka University), Debayan Gupta (Ashoka University)
arXiv:2511. 17038v4 Announce Type: replace Abstract: From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process.
By Hao Chen, Renzheng Zhang, Scott S. Howard
arXiv:2607. 22804v1 Announce Type: cross Abstract: Accurate geological characterization of subsurface reservoirs from well log data is essential to support projects such as carbon capture and storage (CCS), geothermal development, and extraction of natural resources.
By Shwetha Salimath, Francesca Bugiotti, Sylvain Wlodarczyk, Sohaib Ouzineb
arXiv:2606. 14800v1 Announce Type: cross Abstract: This paper reviews how a diverse set of popular data-driven priors commonly used in Bayesian inverse problems can be unified through their respective score functions.
By Elhadji Cisse Faye, Mame Diarra Fall, Sylvain Delchini, Nicolas Dobigeon
arXiv:2605. 08328v3 Announce Type: replace Abstract: Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models.
By Zehua Jiang, Fenghao Zhu, Xinquan Wang, Chongwen Huang, Zhaoyang Zhang
arXiv:2606. 11140v1 Announce Type: cross Abstract: Data assimilation (DA) in subsurface flow entails calibrating model parameters to match observed data, typically at wells, while preserving geological realism.
By Guido Di Federico, Wenchao Teng, Louis J. Durlofsky
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
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