Translational diffusion coefficients D of photochromic dye molecules have been measured by forced Rayleigh scattering in glass forming liquids and polymers at temperatures ranging to below the glass transition Tg. In mixtures where the polymer and diluent component have the same Tg, D is investigated over the whole composition range from pure polymer to pure liquid matrices. In the supercooled liquids, the size of the tracers is similar to that of the surrounding liquid molecules. Thus, we mimic self diffusion which is found to become much faster than predicted by the Stokes‐Einstein relation as the temperature is reduced below a characteristic temperature Tc≳Tg. The crossover temperature Tcagrees with the corresponding temperature determined from neutron scattering experiments and by a power law plot of the shear viscosity as suggested by mode coupling theory. Our finding that translational diffusion behaves different from rotational diffusion which follows the Debye relation down to Tgis discussed in terms of cooperative molecular motion.