Carbon dioxide Capture and Storage (CCS) is an important strategy in mitigating anthropogenic CO$_2$ emissions. In order for CCS to be successful, large quantities of CO$_2$ must be stored and the storage site conformance must be monitored. Here we present a deep learning method to reconstruct pressure fields and classify the flux out of the storage formation based on the pressure data from Above Zone Monitoring Interval (AZMI) wells. The deep learning method is a version of a semi conditional variational auto-encoder tailored to solve two tasks: reconstruction of an incremental pressure field and leakage rate classification. The method, predictions and associated uncertainty estimates are illustrated on the synthetic data from a high-fidelity heterogeneous 2D numerical reservoir model, which was used to simulate subsurface CO$_2$ movement and pressure changes in the AZMI due to a CO$_2$ leakage.