Abstract: Estimation of permeability plays a crucial role in the forecast and risk evaluation of carbon storage operations. In real-world scenarios, direct measurements of permeability and CO$_2$ plume extent are typically sparse due to the high cost. Although inverse modeling approaches allow to estimate the subsurface properties including permeability using observations of other indirect data such as pressure, saturation, and measurements from geophysics, it suffers from expensive computation for large-scale problems. In this work, we test a deep generative prior to sample 3D permeability realizations from a low-dimensional latent space. Then we incorporate the constructed deep generative model to the inverse modeling framework and use observations of saturation to reconstruct the permeability field.