The formation of molecular oxygen in and on amorphous ice in the interstellar medium requires oxygen diffusion to take place. Recent experiments suggest that this process involves quantum tunneling of the oxygen atoms at sufficiently low temperatures. Fitting experimental diffusion rates between 6 and 25 K to an expression that accounts for the roughness of the surface yields excellent agreement. The molecular dynamics of adsorbed oxygen is characterized by rapid intrasite dynamics, followed by intersite transitions over distances of ∼10 Å. Explicit simulations using a realistic free-energy surface for oxygen diffusion on amorphous ice down to 10 K show that quantum tunneling is not required for mobility of adsorbed oxygen. This is confirmed by comparing quantum and classical simulations using the same free-energy surface. The ratio of diffusional and desorption energy Edif/ Edes = 275/1082 ≈ 0.3 is at the lower end of typically used values but is still consistent with the assumptions made in models for interstellar chemistry.