Magnesium alloys use Al and Zn for precipitation hardening, and rare earth elements (Gd, Y, Nd, Ce and La) to randomize texture for improved formability and creep resistance. Controlling processing to obtain these microstructural changes requires accurate knowledge of solute transport. However, current theoretical models to predict diffusivity from atomic jump frequencies make uncontrolled approximations that affect their accuracy. Density-functional theory identifies nine different solute-vacancy configurations from which symmetry analysis determine 17 transitions states corresponding to a 27-frequency model. A new Green function approach computes diffusivity for 14 solutes using the density-functional theory data. We find significant differences for solute drag of Al, Zn, and rare earth solutes, and improved predictions of activation energies for diffusion. The differences with prior predictions can be directly attributed to missing jumps in the 8-frequency model.