Space oceanography missions, especially altimeter missions,have considerably improved the observation of sea surfacedynamics over the last decades. They can however hardlyresolve spatial scales below∼100km. Meanwhile the AIS(Automatic Identification System) monitoring of the mar-itime traffic implicitly conveys information on the underlyingsea surface currents as the trajectory of ships is affected bythe current. Here, we show that an unsupervised variationallearning scheme provides new means to elucidate how AISdata streams can be converted into sea surface currents. Theproposed scheme relies on a learnable variational frame-work and relate to variational auto-encoder approach coupledwith neural ODE (Ordinary Differential Equation) solvingthe targeted ill-posed inverse problem. Through numericalexperiments on a real AIS dataset, we demonstrate how theproposed scheme could significantly improve the reconstruc-tion of sea surface currents from AIS data compared withstate-of-the-art methods, including altimetry-based ones