Monte Carlo random walk simulations of water molecule displacements in realistic cell ensembles are presented. Within an ensemble, the cells have stochastic distributions of sizes, shapes, and interstitial spacings. The probability of molecules permeating the cell membrane is varied. The irreducible, fundamental system parameters are the cell density, ρ, the mean cell volume, <V>, and the steady-state cellular water efflux rate constant, <kio>. Even though the self-diffusion coefficient is that of pure water, non-Gaussian displacements are observed.