  We introduce a schematic non-linear diffusion model where density
fluctuations induce a rich out of equilibrium dynamics. The properties of the
model are studied by numerical simulations and analytically in a mean field
approximation. At low temperatures and high densities we find a long
off-equilibrium glassy region, where the system evolves out of an initially
pinned state showing aging and a slow decay of the autocorrelation as an
enhanced power law, along with strong spatial heterogeneities and violation of
the fluctuation dissipation theorem.
