We simulate nucleation and growth processes of thin films on the basis of the so-called rate equation approach allowing “atoms” to diffuse and rearrange whereby enhancing their co-ordination number. The resulting percolating structures are different from those obtained by the “pure” percolation model where “atomic diffusion” is not taken into account. However, the fractal properties for p = pc are the same as for the percolation model with the fractal dimension of df = 1.896 and for random walks of dw = 2.87. Moreover, df and dw are independent on the diffusion time we choose for our simulations.