High-entropy oxides have recently attracted the interest of the community as a way of attuning the properties of oxides to energy applications. Here, we employ molecular dynamics simulations combined with empirical pair potential models to examine the predicted oxygen diffusivity of fluorite-structured high-entropy oxides. We show that lower levels of the dopants increase the overall diffusivity of the composition, but not to the levels of diffusion seen in yttria-doped zirconia. We attribute this to an increased resistance of the cation sublattice to the distortion that occurs through any multiple substitutions on the cation sublattice. To conclude, it is calculated that oxygen self-diffusion in high-entropy oxides is suppressed as compared to isostructural ternary oxides.