Water in porous silica glass is a suitable system for investigating the effect of confinement on transitional diffusion. These systems are important because of their relevance in catalytic and separation processes. Here quasi-elastic neutron scattering experiments at room temperature on water-filled controlled-pore glasses with radius of 15, 24 and 32 angstroms, are presented and analyzed using the random-jump diffusion model. Both the average residence time and the mean jump distance increase with decreasing pore radius.