The transition from ballistic to electrodiffusive transport of ions through thin polymer membranes has been investigated by recording single transport events via time-correlated single-particle detection. At the highest kinetic energies investigated, ballistic transport of potassium ions is observed with no discernible energy loss to the membrane. At the lowest kinetic energies investigated (several 100 eV) ions are demonstrated to lose the entire kinetic energy to the membrane. Transport there occurs by electrodiffusion. A transition regime is observed. The transition energy is shown to depend on the thickness of the membrane.