Various diffusion processes during sub-monolayer epitaxy of Cu/Cu(100) were studied using the embedded atom method. These processes include (1) single atom diffusion on a flat Cu(100), (2) adatom diffusion around steps running both in [110] and [100] directions, and (3) migration of small clusters of up to 5 atoms on a flat terrace. The results show that the energy barrier for adatom diffusion along the step ledge of [110] directions is actually lower than that for adatom diffusion on a flat terrace and that diffusion across the descending steps depends on step orientation. The exchange mechanism is favored energetically over direct jumps across [110] steps, while direct jumps are favored across [100] steps. Dissociation energies and diffusion barriers for small clusters are oscillatory among clusters of odd and even number atoms. Comparison of dissociation energies and diffusion barriers indicates that (1) tetramers are relatively stable compared to dimers, trimers, and pentamers, and (2) small clusters of up to 5 atoms are quite mobile near room temperature. The calculated results support the conclusions from a recent high-resolution low-energy electron diffraction investigation on sub-monolayer epitaxy for Cu/Cu(100).