[2602.12274] Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage

Computer Science > Machine Learning arXiv:2602.12274 (cs) [Submitted on 12 Feb 2026 (v1), last revised 2 Mar 2026 (this version, v2)] Title:Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage Authors:Xin Ju, Jiachen Yao, Anima Anandkumar, Sally M. Benson, Gege Wen View a PDF of the paper titled Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage, by Xin Ju and 4 other authors View PDF HTML (experimental) Abstract:Accurate characterization of subsurface flow is critical for Carbon Capture and Storage (CCS) but remains challenged by the ill-posed nature of inverse problems with sparse observations. We present Function-space Decoupled Diffusion Posterior Sampling (Fun-DDPS), a generative framework that combines function-space diffusion models with differentiable neural operator surrogates for both forward and inverse modeling. Our approach learns a prior distribution over geological parameters (geomodel) using a single-channel diffusion model, then leverages a Local Neural Operator (LNO) surrogate to provide physics-consistent guidance for cross-field conditioning on the dynamics field. This decoupling allows the diffusion prior to robustly recover missing information in parameter space, while the surrogate provides efficient gradient-based guidance for data assimilation. We demonstrate Fun-DDPS on synthetic CCS modeling datasets, achieving two key results: (1) For forward modeling wit...