In heteroepitaxy, thin-film growth proceeds in two-dimensional layer-by-layer, three-dimensional island, or layer-plus-island modes depending on the growth conditions. Interlayer mass transport plays a crucial role in determining the growth mode. We investigate interlayer diffusion of Au atoms from Au islands grown on Ir(111) by scanning tunneling microscopy (STM) and kinetic Monte Carlo (KMC) simulations. STM measurements reveal that the first Au layer on Ir(111) grows in a complete layer at 100 K, whereas the Au layer grows in a three-dimensional fashion from the second Au layer at this temperature. Annealing these surfaces to 300 K reduces the higher-layer islands, indicating that Au atoms undergo step-down diffusion. By measuring the density of the top-layer islands and comparing them with the KMC simulation results, the additional step-down diffusion barrier for Au atoms to descend from the Au islands is estimated to be 0.02 eV on the first Au layer and 0.04 eV on the second Au layer. The layer dependence of the additional step-down diffusion barrier is explained in terms of the lattice mismatch between Au and underlying layers.