Diffusion of ammonia on Re(001) was studied utilizing optical second harmonic diffraction from surface coverage grating. The diffusion process at initial coverages NH3/Re>0.15 could be simulated only if coverage dependent diffusion constant has been considered. The resulting diffusivity D((theta) )equalsD0 exp(-Em((theta) )/RT), is defined by a barrier for diffusion Em((theta) )equalsE0-(omega) Z(theta) , with activation energy at zero coverage E0equals3.4+/- 0.8 kcal/mol, D0equals2.8(DOT)10-3cm2sec- 1. The repulsion energy between pair of nearest neighbor molecules of (omega) equals0.4+/- 0.06 kcal/mol is obtained if an average of three nearest neighbors is assumed at the edge of the grating. The coverage effect on the diffusivity is found to correlate quantitatively with dipole-dipole repulsion between nearest neighbors. This results in a constant corrugation ratio Ediff/Edes, over the entire coverage range.