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.
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.
arXiv:2607. 04982v1 Announce Type: cross Abstract: High-resolution velocity models are crucial for reservoir characterization and subsurface delineation.
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.
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.
The paper introduces a Posterior‑Dynamics Framework that leverages pretrained diffusion models as multiscale priors for linear imaging inverse problems such as deblurring, super‑resolution, and inpainting. By constructing a surrogate likelihood centered on the clean image and incorporating diffusion uncertainty, the authors derive continuous posterior dynamics and a tunable Langevin component for adaptive exploration. They prove theoretical guarantees (endpoint consistency, finite‑horizon tracking, weak accuracy) and present the PD‑IMEX sampler, which achieves high‑quality reconstructions with only 100 score evaluations and controllable fidelity‑diversity trade‑offs.
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).
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...
arXiv:2607. 21721v1 Announce Type: cross Abstract: Learned generative priors are increasingly used for ill-posed Bayesian inverse problems, their posterior uncertainty treated as earned from data.
arXiv:2606. 03936v1 Announce Type: new Abstract: Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters.
arXiv:2609.14596v1 Announce Type: new Abstract: Training-free diffusion inverse solvers typically choose between local measurement guidance and costly clean-space posterior updates. Independent poste...
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.
Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain.