The diffusion mechanism of a MgO admolecule on a flat MgO(001) surface has been investigated by equilibrium molecular dynamics simulation. Care has been taken in the choice of the phenomenological interionic potential used. Four distinct mechanisms have been found and the corresponding dynamical barriers determined at high temperature. Some static barriers have also been computed for comparison and all intermediate configurations have been obtained with the same phenomenological potential and also by the DFT-GGA approach. The hopping mechanisms involving the Mg adatom, although dominant, must be combined with the infrequent mechanisms involving displacements of O adatoms in order to provide the mass transport on the surface, which is crucial for crystal growth both in the nucleation and step-flow regimes