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Via large scale molecular dynamics simulations, we study diffusion in melts undergoing strong shear flow and its relation to the rheological response in a well established glass forming model system, namely the 80:20 binary Lennard-Jones system first introduced by Kob and Andersen [W. Kob and H.C. Andersen, PRL 73, 1376 (1994)]. In previous works [F. Varnik JCP 125, 164514 (2006) and F. Varnik and O. Henrich PRB 73, 174209 (2006)], the interplay between the dynamics of structural relaxation on the length scale of the average interparticle distance and the stress response of the model was studied. Here we focus on the large scale dynamics under homogeneous shear by evaluating the time dependence of the mean square displacements for temperatures ranging from the supercooled state to far below the mode coupling critical temperature of the model. Particularly long simulations are performed allowing an accurate determination of the diffusion constant. For low temperatures and at not too high shear rates, the mean square displacements exhibit the well known two step relaxation behavior with a long time diffusive motion along the spatial directions perpendicular to the flow. In the flow direction, on the other hand, a third regime follows the diffusive motion, where Taylor dispersion with the typical t3 time dependence clearly dominates the long time behavior of the particle displacements. At the lowest studied temperatures, the cross over from the diffusive regime to the regime where the contribution of Taylor dispersion becomes significant, occurs at length scales of the order of a particle diameter but is shifted towards progressively larger displacements as temperature increases.