Near ambient pressures, molecular diffusion dominates protonic diffusion in ice. Theoretical studies have predicted that protonic diffusion will dominate at high pressures in ice. We measured the protonic diffusion coefficient for the highest temperature molecular phase of ice VII at 400 kelvin over its entire stable pressure region. The values ranged from 10(-17) to 10(-15) square meters per second at pressures of 10 to 63 gigapascals. The diffusion coefficients extrapolated to high temperatures close to the ice VII melting curve were less by a factor of 10(2) to 10(3) than a superionic criterion of approximately 10(-8) square meters per second, at which protons would diffuse freely.