Pulsed magnetic field gradient stimulated echo NMR measurements are performed for diffusion and flow of an aqueous phase both within a sample of packed spherical beads and within a 25% porosity Fontainebleau sandstone. The stimulated echo dependence on the gradient pulse area q is used to derive the displacement probability distributions P-Delta(X) for fixed observation times Delta. The shape of P-Delta(X) as a function of Delta is simulated for computer-generated porous media, and a good agreement is obtained between the experimental NMR data and the simulations.