In this work the validity of generalized Einstein relations, D (ω) = kT/Iβ (ω), where D (ω) and β (ω) are frequency-dependent diffusion and damping coefficients, is examined from a general point of view. It is shown that generalized Smoluchowski (S) equations for both translational and rotational diffusion involving the D (ω), which are defined in terms of simple correlation functions of the fluctuating forces and torques, follow from the appropriate generalized Fokker–Planck (FP) expressions when the translational and angular momenta are taken as rapidly relaxing and a coarse graining in time is introduced. It is found useful in this context to distinguish between those forces and torques fluctuating at rates faster than the diffusive-type motions of the B particle versus those fluctuating more slowly. The appropriate FP equation for rotational diffusion is also derived. Generalized FP and S equations are also derived for the semiclassical case where the molecule(s) examined contains spin degrees of freedom. A proper application of the correspondence principle leads to certain terms referred to as ’’spin-force’’ or ’’spin-torque’’ terms which have the property of tending to restore the spins to their thermal equilibrium value, an important feature usually lacking in semiclassical treatments. Some simple examples of the generalized S equations are given in terms of memory function approximations of the random force and torque correlation functions. The resulting expressions are seen to bear a close formal similarity to typical expressions developed for simple jump models in either orientational or translational space. It is suggested that recent frequency-dependent experiments, including some previously interpreted in terms of simple jump models, may be amenable to analysis in terms of generalized Einstein and S equations.