  We investigate time-dependent stochastic disorder in the one-dimensional
Jaynes-Cummings-Hubbard model and show that it gives rise to diffusive
behaviour. We find that disorder correlation frequency is effective in
controlling the level of diffusivity. In the defectless system the mean squared
displacement (MSD), which is a measure of the diffusivity, increases with
increasing disorder frequency. Contrastingly, when static defects are present
the MSD increases with disorder frequency only at lower frequencies; at higher
frequencies, increasing disorder frequency actually reduces the MSD.
