The diffusion of water confined in a stack of GM3 ganglioside bilayers is studied by computer simulation. A theoretical analysis of the behavior of the mean square displacement parallel and perpendicular to the bilayer surface is also provided in terms of diffusion equations in a very long time interval, between 2 ps and 2 ns. Such an analysis has allowed us to identify two different time regimes, to clarify the nature of nonlinear time dependence of the mean square displacement, and to give an interpretation to the origin of the often used time dependent diffusion coefficient. Both the effects of spatial inhomogeneities and boundary conditions are demonstrated to be the key points for the interpretation of all these results within a consistent theoretical framework.