[2509.21659] RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion

Computer Science > Machine Learning arXiv:2509.21659 (cs) [Submitted on 25 Sep 2025 (v1), last revised 1 Mar 2026 (this version, v2)] Title:RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion Authors:Siming Shan, Min Zhu, Youzuo Lin, Lu Lu View a PDF of the paper titled RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion, by Siming Shan and 3 other authors View PDF HTML (experimental) Abstract:Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here, we introduce a new computational framework, RED-DiffEq, by integrating physics-driven inversion and data-driven learning. RED-DiffEq leverages pretrained diffusion models as a regularization mechanism for PDE-governed inverse problems. We apply RED-DiffEq to solve the full waveform inversion problem in geophysics, a challenging seismic imaging technique that seeks to reconstruct high-resolution subsurface velocity models from seismic measurement data. Our method shows enhanced accuracy and robustness compared to conventional methods. Additionally, it exhibits strong generalization ability to more complex velocity models that the diffusion model is not trained on. Our framework can also be...