In this Letter, we explore the relations between tracer diffusion and flow heterogeneities in amorphous materials. On the basis of scaling arguments and an extensive numerical study of an athermal elastoplastic model, we show that there is a direct link between the self-diffusion coefficient and the size of cooperative regions at low strain rates. Both depend strongly on rate and system size. The mean square displacement of passive tracers thus gives information about the microscopic rheology, such as the geometry of cooperative regions and their scaling with strain rate and system size.