The results of a recently presented theory for polymer dynamics are compared with experimental diffusion constant data for polyethylene, poly (ethylene oxide), and poly (dimethyl siloxane) polymer melts. The molecular weight dependence of the self-diffusion constants for these systems is investigated. The various constants that appear in the theory are optimized using theoretical analysis and published results from computer simulations. The only adjustable parameters for each system are the friction coefficients for lateral and reptative motions. It is found that the same ratio of the monomer friction coefficients for lateral and reptative motions can be employed for all three experimental systems and for the two computer simulation systems considered. This is reasonable, since all these systems have fairly simple monomer units without large side groups. This leaves the monomer friction coefficient for lateral motions as the only system-dependent adjustable parameter in these calculations. Excellent agreement is found between the predictions of the theory and the experimental data.