Results are presented for the self-diffusion properties of monodisperse n-alkanes and cis-1,4 polyisoprene (PI) oligomer melts, as obtained through detailed atomistic molecular dynamics (MD) simulations. The simulations have been conducted in the NVT statistical ensemble on model systems thoroughly pre-equilibrated through an efficient Monte Carlo (MC) algorithm. Results for the self-diffusion coefficient D as a function of molecular weight M support a scaling law of the form D similar toM(b), with b strongly depending on temperature T, for both the n-alkanes and the cis-1,4 PI melts. The simulation results have been fitted to an expression for D involving elements of Rouse dynamics and Cohen-Turnbull-Bueche chain-end (excess free volume) effects, proposed recently by von Meerwall [J. Chem. Phys. 108, 4299 (1998)]. Using a geometric analysis involving tessellation of space in Delaunay tetrahedra developed by Greenfield and Theodorou [Macromolecules 26, 5461 (1993)], we have also calculated the excess chain-end free volume of the alkane and cis-1,4 PI melts. Calculated self-diffusivities and apparent activation energies for the two different polymers as a function of their molecular weight M are in excellent agreement with the experimental measurements of von Meerwall (1998).