3He spin-echo measurements are used to follow the picosecond motion of sodium atoms on a copper (001) substrate. 2D correlated motion arising from repulsive adsorbate interactions is observed for coverages as low as 0.04 ML. At coverages greater than 0.05 ML there is a pronounced onset of motion perpendicular to the surface. The perpendicular motion is thermally activated and seems related to the basic translational hopping diffusion process. The correlated motion is modeled successfully using a molecular dynamics simulation and a dipolelike lateral interaction. A simple model which relates the apparent height of the atom with its local coverage is shown to reproduce the experimental observations.