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We discuss a generalization of the Haken-Strobl-Reineker model for the diffusion coefficient of a particle ͑or an excitation͒ in a one-dimensional lattice. In the original treatment, the characteristic correlation time of the lattice vibrations is assumed to be the smallest time scale in the physical problem. We weaken this requirement and allow for longer correlation times. We discuss previous results in the context of our theory and present numerical examples.doi:10.1103/physrevb.62.3744 fatcat:tooaotcm5fdltieo4qbvir7nvy