Accurate modeling of CO₂ storage in the subsurface is a critical challenge for scaling Carbon Capture and Storage (CCS). 🌎 But here’s the catch: the inverse problem (recovering geological properties from sparse field observations) is severely ill-posed. 🤒 Traditional approaches either struggle with the scarcity of measured data or are too computationally expensive. 💸 In our new work, we introduce Fun-DDPS (Function-space Decoupled Diffusion Posterior Sampling), a generative framework that decouples the problem into two parts: a function-space diffusion model that learns a prior over geological parameters, and a differentiable Local Neural Operator surrogate for physics modeling and conditioning. ✨ Why does the decoupling matter? The diffusion prior handles the heavy lifting of recovering missing geological information, while the neural operator surrogate makes data assimilation fast and physically grounded — no expensive full-physics simulations in the loop. Key results on synthetic CCS datasets: ⏩ 11x improvement in forward modeling with only 25% observations ✅ Robust inverse modeling for data assimilation under sparse, noisy conditions 🔥 First rigorous validation of diffusion-based inverse solvers against asymptotically exact Rejection Sampling (RS) posteriors This points toward a scalable, practical path for uncertainty-aware subsurface characterization — something the CCS community needs as projects move from pilots to full-scale deployment. 📷 Huge kudos to my amazing collaborators — this work wouldn’t have been possible without them: @IsaacJu13 @AnimaAnandkumar Sally M Benson @ggg_www_ #CarbonCapture# #CO2Sequestration# #MachineLearning# #DiffusionModels# #NeuralOperators# #AI4Science# #CCS# #Sustainability#