Previous results giving the diffusion coefficient for an exciton or charge carrier in a perfect molecular crystal in both the band and the hopping regime, and interpolating between regimes, are evaluated with and without nonlocal electron‐phonon coupling to second order. Nonlocal coupling produces an extra contribution to the hopping rate; it may increase or decrease the usual scattering rate, depending on the relative signs of local and nonlocal coupling, but changes the transfer rate in the opposite direction through the phonon displacements in the polaron states produced by local coupling. Increasing the temperature decreases the importance of nonlocal coupling in the band regime but increases it in the hopping regime. The significance of these effects depends on the detailed coupling model. The enhanced hopping rate agrees with previous published work.