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

• URL: http://arxiv.org/abs/2602.12274v1
• Date: Thu, 12 Feb 2026 18:58:12 GMT
• 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,
• Abstract summary: We present Fun-DDPS, a generative framework that combines function-space diffusion models with differentiable neural operator surrogates for both forward and inverse modeling.<n>Fun-DDPS produces physically consistent realizations free from the high-frequency artifacts observed in joint-state baselines.
• Score: 65.51149575007149
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

Related papers

• Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction [45.25461515976432]
  Plug-and-Play diffusion prior (DP) frameworks have emerged as a powerful paradigm for imaging reconstruction.<n>We present a novel approach to resolving bias-hallucination trade-off, achieving state-of-the-art gradients with significantly accelerated convergence.
  arXiv  Detail & Related papers  (2026-02-26T16:58:43Z)
• Robust Inference-Time Steering of Protein Diffusion Models via Embedding Optimization [6.097829741846035]
  EmbedOpt is an inference-time approach for steering diffusion models to optimize experimental likelihoods in the conditional embedding space.<n>We show that EmbedOpt outperforms the coordinate-based posterior sampling method in map fitting tasks and matches performance on distance constraint tasks.
  arXiv  Detail & Related papers  (2026-02-05T04:13:33Z)
• Decoupled Diffusion Sampling for Inverse Problems on Function Spaces [73.52103661482242]
  Existing plug-and-play diffusion posterior samplers represent physics implicitly through coefficient joint-solution modeling.<n>We propose a physics-aware generative framework in function space for inverse PDE problems.<n>Our Decoupled Diffusion Inverse Solver (DDIS) employs a decoupled design: an unconditional diffusion learns the coefficient prior, while a neural operator explicitly models the forward PDE for guidance.
  arXiv  Detail & Related papers  (2026-01-30T18:54:49Z)
• Efficient Federated Learning with Heterogeneous Data and Adaptive Dropout [62.73150122809138]
  Federated Learning (FL) is a promising distributed machine learning approach that enables collaborative training of a global model using multiple edge devices.<n>We propose the FedDHAD FL framework, which comes with two novel methods: Dynamic Heterogeneous model aggregation (FedDH) and Adaptive Dropout (FedAD)<n>The combination of these two methods makes FedDHAD significantly outperform state-of-the-art solutions in terms of accuracy (up to 6.7% higher), efficiency (up to 2.02 times faster), and cost (up to 15.0% smaller)
  arXiv  Detail & Related papers  (2025-07-14T16:19:00Z)
• Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence [0.44241702149260353]
  We apply four generative diffusion modeling approaches to super-resolution and inference of quasi-geostrophic turbulence on the beta-plane.<n>We consider eight test cases spanning: two regimes, eddy and anisotropic-jet turbulence; two Reynolds numbers, 103 and 104; and two observation types, 4x coarse-resolution fields and coarse, sparse and gappy observations.<n>Results show that SDEdit generates unphysical fields, while DPS generates reasonable reconstructions at low computational cost but with smoothed fine-scale features.
  arXiv  Detail & Related papers  (2025-07-01T12:59:10Z)
• Guided Diffusion Sampling on Function Spaces with Applications to PDEs [112.09025802445329]
  We propose a general framework for conditional sampling in PDE-based inverse problems.<n>This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning.<n>Our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines.
  arXiv  Detail & Related papers  (2025-05-22T17:58:12Z)
• ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model [5.24776944932192]
  We introduce the Information-Theoretic Discrete Poisson Diffusion Model (ItDPDM), inspired by photon arrival process.<n>Central to our approach is an information-theoretic Poisson Reconstruction Loss (PRL) that has a provable exact relationship with the true data likelihood.<n>ItDPDM attains superior likelihood estimates and competitive generation quality-demonstrating a proof of concept for distribution-robust discrete generative modeling.
  arXiv  Detail & Related papers  (2025-05-08T09:29:05Z)
• Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
  Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
  arXiv  Detail & Related papers  (2024-07-25T09:53:12Z)
• DiffPuter: Empowering Diffusion Models for Missing Data Imputation [56.48119008663155]
  This paper introduces DiffPuter, a tailored diffusion model combined with the Expectation-Maximization (EM) algorithm for missing data imputation.<n>Our theoretical analysis shows that DiffPuter's training step corresponds to the maximum likelihood estimation of data density.<n>Our experiments show that DiffPuter achieves an average improvement of 6.94% in MAE and 4.78% in RMSE compared to the most competitive existing method.
  arXiv  Detail & Related papers  (2024-05-31T08:35:56Z)
• Robust Bayesian Inference for Discrete Outcomes with the Total Variation Distance [5.139874302398955]
  Models of discrete-valued outcomes are easily misspecified if the data exhibit zero-inflation, overdispersion or contamination. Here, we introduce a robust discrepancy-based Bayesian approach using the Total Variation Distance (TVD) We empirically demonstrate that our approach is robust and significantly improves predictive performance on a range of simulated and real world data.
  arXiv  Detail & Related papers  (2020-10-26T09:53:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.