Detecting and characterizing slow slip events (SSEs) in Global Navigation Satellite System (GNSS) time series is challenging and multi-station deep-learning approaches are still little explored. The main difficulty is the high level of noise in GNSS time series. The noise affecting GNSS measurements is spatially and temporally correlated, which requires setting up multi-station methods to better characterize the spatial extent of slow slip events. Here, we develop and compare different deep-learning approaches to detect and characterize SSEs in GNSS data, showing that methods embedding the spatial information outperform time-series-based approaches, with spatiotemporal models being the most promising and flexible on real GNSS data.