We study proton diffusion in amorphous SiO2 and hafnium silicates at the atomic scale. In amorphous SiO2, ab initio molecular dynamics suggest that the dominant atomic process consists in cross-ring interoxygen hopping assisted by network vibrations. In hafnium silicates, we find that the proton localizes on O atoms bonded to Hf atoms, in accord with our static total-energy calculations. These results imply that in stacked gate oxides the proton preferentially localizes within the high-kappa oxide rather than within the SiO2 interlayer.