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Wang et al. [PNAS 106 (2009) 15160] have found that in several systems thelinear time dependence of the mean-square displacement (MSD) of diffusingcolloidal particles, typical of normal diffusion, is accompanied by anon-Gaussian displacement distribution (DisD), with roughly exponential tailsat short times, a situation they termed "anomalous yet Brownian" diffusion. Thediversity of systems in which this is observed calls for a generic model. Wepresent such a model where there is "diffusivity memory" but no "directionmemory" in the particle trajectory, and we show that it leads to both a linearMSD and a non-Gaussian DisD at short times. In our model, the diffusivity isundergoing a (perhaps biased) random walk, hence the expression "diffusingdiffusivity". The DisD is predicted to be exactly exponential at short times ifthe distribution of diffusivities is itself exponential, but an exponentialremains a good fit to the DisD for a variety of diffusivity distributions.Moreover, our generic model can be modified to produce subdiffusion.

"Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion