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

TL;DR

This paper introduces Fun-DDPS, a novel diffusion-based framework combining function-space models and neural surrogates for accurate, data-efficient forward and inverse modeling in subsurface flow for CCS, especially under sparse observations.

Contribution

The paper presents a new decoupled diffusion framework that improves subsurface modeling accuracy and efficiency, validated against rigorous benchmarks and outperforming existing methods under data scarcity.

Findings

Achieves 7.7% relative error with 25% observations, outperforming standard surrogates.

First validation of diffusion inverse solvers against asymptotic Rejection Sampling.

Produces physically consistent realizations with 4x sample efficiency over rejection sampling.

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 with only 25% observations, Fun-DDPS achieves 7.7% relative error compared to 86.9% for standard surrogates (an 11x improvement), proving its capability to handle extreme data sparsity where deterministic methods fail. (2) We provide the first rigorous validation of diffusion-based inverse solvers against asymptotically exact Rejection Sampling (RS) posteriors. Both Fun-DDPS and the joint-state baseline (Fun-DPS) achieve Jensen-Shannon divergence less than 0.06 against the ground truth. Crucially, Fun-DDPS produces physically consistent realizations free from the high-frequency artifacts observed in joint-state baselines, achieving this with 4x improved sample efficiency compared to rejection sampling.