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. 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:2607. 04982v1 Announce Type: cross Abstract: High-resolution velocity models are crucial for reservoir characterization and subsurface delineation.
By Francesco Brandolin, Tariq Alkhalifah
arXiv:2509.19276v2 Announce Type: replace-cross
Abstract: Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this t...
By Tim Y. J. Wang, O. Deniz Akyildiz
The paper introduces tunable latent priors for diffusion models, normalizing flows, and variational autoencoders using nested dropout. These priors allow the latent dimensionality to adapt to each inverse problem, reducing reconstruction errors compared to fixed-complexity models across tasks such as compressed sensing, inpainting, denoising, and phase retrieval. In linear denoising, the authors derive the optimal latent complexity in closed form, linking it to noise level and signal spectrum.
By Sean Gunn, Jorio Cocola, Oliver De Candido, Vaggos Chatziafratis, Paul Hand
arXiv:2603. 00393v2 Announce Type: replace-cross Abstract: Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy, incomplete data or inherent non-uniqueness.
By Ali Siahkoohi, Kamal Aghazade, Ali Gholami
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.
By Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune, Marcello Carioni
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 Sensitivity‑Constrained Neural Operators (SC‑NOs), which augment standard neural operator training with sampled Jacobian supervision from differentiable solvers or discrete adjoints. By matching selected sensitivities during training, SC‑NOs improve forward prediction accuracy and significantly enhance gradient‑based inverse reconstruction for distributed fields. Experiments on advection–diffusion, RANS–Spalart–Allmaras, high‑dimensional gridded inputs, and a shallow‑water tsunami source‑inversion case demonstrate that SC‑NOs achieve a better accuracy–cost trade‑off and enable near‑real‑time wave‑propagation forecasting from sparse observations.
By Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer, Kathryn Lawson
HarmoCore introduces a generative prior in a compact, continuous latent space for reconstructing oscillatory wave fields from extremely sparse sensor data. It models joint real–imaginary channels using Functional Tucker cores over shared spatial bases, learns a frequency‑conditioned diffusion prior, and performs diffusion posterior sampling directly in core space. Experiments on 2D and 3D Helmholtz problems demonstrate significant performance gains with only 1%–2% sensor coverage while remaining scalable to three dimensions.
By Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang
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