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