We use a combined experimental and theoretical approach to study the rates of surface diffusion processes that govern early stages of thin Ag and Cu film morphological evolution on weakly-interacting amorphous carbon substrates. Films are deposited by magnetron sputtering, at temperatures TS between 298 and 413 K, and vapor arrival rates F in the range 0.08 to 5.38 monolayers/s. By employing in situ and real-time sheet-resistance and wafer-curvature measurements, we determine the nominal film thickness Θ at percolation (Θperc) and continuous film formation (Θcont) transition. Subsequently, we use the scaling behavior of Θperc and Θcont as a function of F and Ts, to estimate, experimentally, the temperature-dependent diffusivity on the substrate surface, from which we calculate Ag and Cu surface migration energy barriers [Formula: see text] and attempt frequencies [Formula: see text]. By critically comparing [Formula: see text] and [Formula: see text] with literature data, as well as with results from our ab initio molecular dynamics simulations for single Ag and Cu adatom diffusion on graphite surfaces, we suggest that: (i) [Formula: see text] and [Formula: see text] correspond to diffusion of multiatomic clusters, rather than to diffusion of monomers; and (ii) the mean size of mobile clusters during Ag growth is larger compared to that of Cu. The overall results of this work pave the way for studying growth dynamics in a wide range of technologically-relevant weakly-interacting film/substrate systems-including metals on 2D materials and oxides-which are building blocks in next-generation nanoelectronic, optoelectronic, and catalytic devices.