Self-diffusion in water, occupying 25% of the pore space within a random packing of 100 mum diameter glass beads, is characterised using pulsed field gradient spin echo (PGSE) NMR to determine the joint probability, P-Delta(X, Y) of displacements X and Y in time Delta. It is demonstrated that the detailed features exhibited by the correlation distribution C-Delta(X, Y)[= P-Delta(X, Y) - P-Delta (X)P-Delta(Y)] reflect the anisotropic microscopic structures of the water phase despite the overall isotropy of the sample. It is suggested that this will allow detailed structural characterisation of restricting environments, such as porous solids, via the diffusion and flow of contained fluids.