We study water dynamics at a silica aqueous interface. Both hydrophilic (hydroxylated) surfaces and hydrophobic surfaces (dehydroxylated upon irradiation) have been generated from atomistic simulations. A new method for the calculation of the normal self-diffusion coefficients based on the calculation of mean first passage times is proposed. It uses the Smoluchowski theory of Brownian motion and it takes proper account of the layering of the molecules. In the case of parallel self-diffusion coefficients, a decrease is found compared to the bulk values. It can be described in terms of hydrodynamic boundary conditions induced by the surface confinement. This hydrodynamic explanation is not enough to interpret the case of normal self-diffusion coefficients for which an important diminution is found. Normal self-diffusion coefficients appear to depend strongly on the hydrophilicity of the surface. They tend towards their bulk value only at long distances from the surfaces. The first layer of water molecules is found to be partially adsorbed.