Diffusion of substrate material to the surface of some epitaxial thin-film systems has been reported to occur very rapidly, even at temperatures below 40% of the melting points of film and substrate, where bulk interdiffusion should be negligible. In situ scanning tunneling microscopy reveals that the Cu diffusion through ultrathin Co films grown under ultrahigh vacuum onto Cu(100) substrates occurs via a surface diffusion process, not via bulk interdiffusion. During annealing, pores nucleate in weak points of the films, e.g. near step bands of the substrate. As Cu diffuses from the substrate through the pores to the top of the film, pits of up to several tens of nm linear dimensions are formed.