The single particle dynamics of a 2D liquid made up of soft disks interacting by a repulsive r(-12) potential are studied using molecular dynamics simulations. We find that mean squared particle displacement [Delta r(t)(2)] behaves diffusively, i.e., increases linearly with time, within a time interval t(c) very much shorter than that required for structural relaxation. The non-Gaussian parameter alpha(t)=[Delta r(4)]/2[Delta r(2)](2)-1, on the other hand, exhibits a significant peak at times considerably greater than t(c) and a subsequent slow decay. It is argued that the only picture of diffusion consistent with these results considers particles moving in a medium characterized by fluctuating local mobilities. This picture provides an explicit connection between structural fluctuations (as characterized by the local mobility) and single particle motion. The possibility of obtaining the width and lifetime of the distribution of local relaxation times from incoherent scattering is examined.