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.

翻译：精确刻画地下流体运移对碳捕集与封存至关重要，但受限于稀疏观测数据导致反问题的不适定性，该任务仍面临挑战。本文提出Fun-DDPS生成式框架，将函数空间扩散模型与可微分神经算子代理模型相结合，实现正反演联合建模。该方法通过单通道扩散模型学习地质参数（地质模型）的先验分布，并利用局部神经算子代理模型为动力学场的跨场条件提供物理一致性指导。这种解耦设计使扩散先验能稳健恢复参数空间的缺失信息，同时代理模型为数据同化提供高效的梯度引导。我们在合成CCS建模数据集上验证Fun-DDPS，取得两项关键成果：（1）在仅25%观测数据的正演建模中，Fun-DDPS相对误差为7.7%，而标准代理模型误差达86.9%（提升11倍），证明其在确定性方法失效的极端数据稀疏场景下的有效性。（2）首次基于渐近精确的拒绝采样后验分布，对扩散反演求解器进行严格验证。Fun-DDPS与联合状态基线方法均获得小于0.06的Jensen-Shannon散度值。关键的是，Fun-DDPS生成的实现具有物理一致性，避免了联合状态基线中出现的高频伪影，且采样效率较拒绝采样提升4倍。