The diffusion of water in mixtures of water and poly(vinyl alcohol) (0-97%) has been investigated using atomistic molecular dynamics simulation. The dependence of the calculated diffusion coefficients on the polymer concentration follows the Mackie-Meares equation to a good approximation. It is found that the pattern of water diffusion undergoes a pronounced change with concentration and temperature. It changes from a random walk (pure water) to a hopping mechanism (high polymer concentration) with combinations of the two extremes at intermediate concentrations. The hopping mechanism possibly leads to anomalous diffusion at lengths scales comparable to the thickness of the active layer of the membrane.