The motion of molecules on solid surfaces is of interest for technological applications such as catalysis and lubrication, but it is also a theoretical challenge at a more fundamental level. The concept of activation barriers is very convenient for the interpretation of experiments and as input for Monte Carlo simulations but may become inadequate when mismatch with the substrate and molecular vibrations are considered. We study the simplest objects diffusing on a substrate at finite temperature T, namely an adatom and a diatomic molecule (dimer), using the Langevin approach. In the driven case, we analyze the characteristic curves, comparing the motion for different values of the intramolecular spacing, both for T=0 and Tnot equal0. The mobility of the dimer is higher than that of the monomer when the drift velocity is less than the natural stretching frequency. The role of intramolecular excitations is crucial in this respect. In the undriven case, the diffusive dynamics is considered as a function of temperature. Contrary to atomic diffusion, for the dimer it is not possible to define a single, temperature independent, activation barrier. Our results suggest that vibrations can account for drastic variations of the activation barrier. This reveals a complex behaviour determined by the interplay between vibrations and a temperature dependent intramolecular equilibrium length.