In low-viscosity liquids, diffusion is inversely related to viscosity via the Stokes-Einstein relation. However, the Stokes-Einstein relation breaks down near the glass transition as the supercooled liquid transitions into the non-ergodic glassy state. The nonequilibrium viscosity of glass is governed by the liquid-state viscous properties, namely, the glass transition temperature and the fragility. Here, a model is derived to predict the ionic diffusivity of a glass from its nonequilibrium viscosity, accounting for the compositional dependence of the glass. The free energy activation barrier for diffusion is related to the activation enthalpy for viscous flow using the Mauro-Allan-Potuzak model of nonequilibrium viscosity [Mauro, J. C.; Allan, D. C.; Potuzak, M. Nonequilibrium Viscosity of Glass. Phys. Rev. B 2009, 80, 094204]. These insights allow for accurate prediction of activation barriers for diffusion of alkali ions. The model is supported by experimental results and nudged-elastic band calculations applied to sodium silicate and borate glasses.