Reducing CO$_2$ emissions is crucial to mitigating climate change. Carbon Capture and Storage (CCS) is one of the few technologies capable of achieving net-negative CO$_2$ emissions. However, predicting fluid flow patterns in CCS remains challenging due to uncertainties in CO$_2$ plume dynamics and reservoir properties. Building on existing seismic imaging methods like the Joint Recovery Method (JRM), which lacks uncertainty quantification, we propose the Probabilistic Joint Recovery Method (pJRM). By estimating posterior distributions across surveys using a shared generative model, pJRM provides uncertainty information to improve risk assessment in CCS projects.