The diffusion of water in a saturated porous medium formed by close-packed monodisperse polystyrene hard spheres has been studied using pulsed gradient spin-echo nuclear magnetic resonance. The echo-attenuation data from three different sphere systems, obtained using a range of diffusive observation times, are analyzed using an analytic function based on a pore-hopping model. We show that diffraction-like coherence peaks, which arise in the echo attenuation, are strongly influenced by sphere size and polydispersity, and that realistic structural parameters can be obtained from the fits to the data.