The self-diffusion coefficient (D) of liquid CS2 has been determined by computer simulation for seven densities (rho) and eight temperatures, spanning more than two decades of D in the supercooled and near-melting normal liquid, and bracketing the P=1 atm isobar. Super-Arrhenius behavior of -log D vs 1/T, an increase in slope with decreasing T, is found at 1 atm, but normal Arrhenius T dependence holds along all seven different isochores, even at the highest density and lowest T. The super-Arrhenius behavior is a consequence of the variation in density rho(T) at constant pressure. Physically meaningful activation energies, representative of the heights of the barriers to diffusion, depend upon rho only, are smaller than the isobaric slope, and may be obtained by correcting it or from an Arrhenius plot at constant density. Barriers to diffusion are indeed higher at lower temperatures, but only due to the higher density. The importance of T vs rho as the "control variable" for diffusion is examined. Temperature and density play comparable roles near the melting states, and the relative importance of T grows with supercooling. However that growth is due to the higher activation energy, itself controlled by density.