Starting from a classical mechanical model, a set of Langevin equations for the surface diffusion of adsorbed molecules is developed. In contrast to previous work, these Langevin equations take full account of the rotations and internal vibrations of the adsorbed molecule. These equations are then applied to a stiff dimer diffusing in one dimension, and the results compared with previous calculations for the same system. It is shown that the modifications in our new approach give significantly different results than this previous calculation, and therefore must be taken into account in future calculations for systems of this kind. Next a new approximation method is developed by assuming that the motion of the molecule is confined to the lowest energy path between adsorption sites. This method is applicable to an arbitrarily complex molecule, and is complimentary to the first method, in that it can account for deformation of the molecule by the surface but not the internal vibrations of the molecule (whereas the first method accounts for internal vibrations but not deformation). This approximation method is then applied to a flexible dimer in two dimensions (one dimension along the surface and one perpendicular). The results are discussed and compared with those of the stiff dimer in one dimension, explaining and clarifying the difference between our results and those of previous calculations.