  Diffusion of a particle in the N-dimensional external potential which is
periodic in one dimension and unbounded in the other N-1 dimensions is
investigated. We find an analytical expression for the overdamped diffusion and
study numerically the cases of moderate and low damping. We show that in the
underdamped limit, the multi-dimensional effects lead to reduction (comparing
with the one-dimensional motion) of jump lengths between subsequent trapping of
the atom in bottoms of the external periodic potential. As application we
consider the diffusion of a dimer adsorbed on the crystal surface.
