The Stokes--Einstein relation (SER) is one of most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for selfsolvation which cannot be explained by the standard hydrodynamic derivation. Here we revisit the work of Masters and Madden [J. Chem. Phys. 74 2450-2459 (1981)] who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents we identify a potential microscopic origin of some of these deviations. We also reproduce the SER result from the exact dynamics of infinite-dimensional fluids.
