We present results of molecular dynamics (MD) simulations and density functional theory (DFT) calculations of the diffusion of Cu adatom and dimer on Ag(111). We have used potentials generated by the embedded-atom method for the MD simulations and pseudopotentials derived from the projected-augmented-wave method for the DFT calculations. The MD simulations (at three different temperatures: 300, 500, and 700 K) show that the diffusivity has an Arrhenius behavior. The effective energy barriers obtained from the Arrhenius plots are in excellent agreement with those extracted from scanning tunneling microscopy experiments. While the diffusion barrier for Cu monomers on Ag(111) is higher than that reported (both in experiment and theory) for Cu(111), the reverse holds for dimers [which, for Cu(111), has so far only been theoretically assessed]. In comparing our MD result with those for Cu islets on Cu(111), we conclude that the higher barriers for Cu monomers on Ag(111) results from the comparatively large Ag-Ag bond length, whereas for Cu dimers on Ag(111) the diffusivity is taken over and boosted by the competition in optimization of the Cu-Cu dimer bond and the five nearest-neighbor Cu-Ag bonds. Our DFT calculations confirm the relatively large barriers for the Cu monomer on Ag(111)-69 and 75 meV-compared to those on Cu(111) and hint a rationale for them. In the case of the Cu dimer, the relatively long Ag-Ag bond length makes available a diffusion route whose highest relevant energy barrier is only 72 meV and which is not favorable on Cu(111). This process, together with another involving an energy barrier of 83 meV, establishes the possibility of low-barrier intercell diffusion by purely zigzag mechanisms. © 2010 The American Physical Society.