  We consider the diffusion of markers in a layered medium, with the lateral
diffusion coefficient being the function of hight. We show that the probability
density of the lateral displacements follows one-dimensional Batchelor's
equation with time-dependent diffusion coefficient governed by the particles'
redistribution in height. For the film of a finite thickness the resulting mean
squared displacement exhibits superdiffusion at short times and crosses over to
normal diffusion at long times. The approach is used for description of
experimental results on inhomogeneous molecular diffusion in thin liquid films
deposited on solid surfaces.
