We discuss a generalization of the Haken-Strobl-Reineker model for the diff
usion coefficient of a particle (or an excitation) in a one-dimensional lat
tice. In the original treatment, the characteristic correlation time of the
lattice vibrations is assumed to be the smallest time scale in the physica
l problem. We weaken this requirement and allow for longer correlation time
s. We discuss previous results in the context of our theory and present num
erical examples.