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

Source: arXiv - 2602.12274v1

Overview

A new generative framework called Fun‑DDPS tackles one of the toughest challenges in carbon capture and storage (CCS): reliably predicting how CO₂ moves underground when we only have a handful of noisy measurements. By marrying a diffusion‑based prior over geological models with a fast neural‑operator surrogate of the physics, the authors achieve dramatically better forward predictions and a principled way to invert for hidden subsurface properties.

Key Contributions

• Function‑space diffusion prior that learns a realistic distribution of geological parameters (e.g., permeability fields) from a single training channel.
• Local Neural Operator (LNO) surrogate that provides differentiable, physics‑consistent gradients for conditioning the diffusion model on observed flow data.
• Decoupled forward/inverse pipeline that separates the learning of the prior (parameter space) from the data‑assimilation step (state space), avoiding the high‑frequency artifacts seen in joint‑state approaches.
• Rigorous validation against asymptotically exact Rejection Sampling posteriors, showing Jensen‑Shannon divergence < 0.06 and a 4× boost in sample efficiency.
• Extreme data‑sparsity robustness: with only 25 % of the flow field observed, forward predictions drop from ~87 % error (standard surrogates) to < 8 % error.

Methodology

1. Learn a Prior in Function Space

   • A single‑channel diffusion model is trained on many synthetic geological realizations (e.g., permeability maps).
   • The diffusion process gradually adds noise to a geomodel and learns to reverse it, yielding a generative prior that can sample plausible subsurface structures.

2. Physics‑Guided Conditioning via a Neural Operator

   • A Local Neural Operator (LNO) is trained to emulate the governing PDEs of CO₂ flow (Darcy’s law, transport equations).
   • Because the LNO is differentiable, it can compute gradients of a data‑misfit loss with respect to the latent geomodel, enabling gradient‑based guidance during diffusion sampling.

3. Decoupled Sampling for Forward & Inverse Tasks

   • Forward modeling: Sample a geomodel from the diffusion prior, then push it through the LNO to generate the full flow field, even when only sparse observations are available.
   • Inverse modeling: Condition the diffusion prior on the observed flow field using the LNO gradients, effectively “pulling” the sampled geomodels toward those that reproduce the measurements.

4. Training & Inference Pipeline

   • The diffusion prior and LNO are trained separately on synthetic datasets, which simplifies optimization and allows each component to specialize.
   • At inference time, a few gradient‑descent steps (guided by the LNO) are enough to steer the diffusion sampler toward high‑posterior‑probability samples.

Results & Findings

• Physical realism: Fun‑DDPS samples respect the underlying PDE constraints, avoiding the spurious high‑frequency noise that plagued joint‑state diffusion baselines.
• Sample efficiency: The decoupled approach reaches the same posterior quality as Rejection Sampling with a fraction of the computational budget.

Practical Implications

• Reduced monitoring costs: Operators can obtain accurate plume forecasts even when only a quarter of the usual sensor network is deployed, cutting hardware and drilling expenses.
• Faster decision loops: The LNO surrogate runs orders of magnitude faster than full finite‑element simulators, enabling near‑real‑time scenario testing for injection strategies or leak detection.
• Robust risk assessment: By providing a calibrated posterior over hidden geological properties, the method supports probabilistic risk quantification (e.g., probability of breach or unintended migration).
• Plug‑and‑play workflow: Since the diffusion prior and neural operator are trained separately, existing CCS simulators can be swapped in for the LNO, making integration into legacy pipelines straightforward.
• Generalizable to other subsurface problems: The same decoupled diffusion‑operator recipe could be applied to groundwater remediation, geothermal reservoir management, or oil‑field forecasting where data are sparse but physics are well‑understood.

Limitations & Future Work

• Synthetic‑only validation: Experiments were performed on generated datasets; real‑world field data may introduce noise patterns and heterogeneities not captured in training.
• Single‑channel diffusion: The current prior models only one geological field (e.g., permeability). Extending to multi‑field priors (porosity, caprock strength) could improve realism.
• Scalability to very large domains: While the LNO is local, diffusion sampling still requires multiple passes over the entire domain; hierarchical or multi‑resolution diffusion could reduce memory footprints.
• Uncertainty in physics: The surrogate assumes perfect knowledge of governing equations. Future work could incorporate model‑form uncertainty (e.g., uncertain relative permeability curves) into the diffusion conditioning loop.

Bottom line: Fun‑DDPS demonstrates that a clever split between a learned prior and a differentiable physics surrogate can turn a notoriously ill‑posed inverse problem into a tractable, data‑efficient workflow—opening the door for more agile, cost‑effective CCS operations.

Authors

• Xin Ju
• Jiachen Yao
• Anima Anandkumar
• Sally M. Benson
• Gege Wen

Paper Information

• arXiv ID: 2602.12274v1
• Categories: cs.LG, physics.geo-ph
• Published: February 12, 2026
• PDF: Download PDF