  A mass ejection model in a time-dependent random environment with both
temporal and spatial correlations is introduced. When the environment has a
finite correlation length, individual particle trajectories are found to
diffuse at large times with a displacement distribution that approaches a
Gaussian. The collective dynamics of diffusing particles reaches a
statistically stationary state, which is characterized in terms of a
fluctuating mass density field. The probability distribution of density is
studied numerically for both smooth and non-smooth scale-invariant random
environments. A competition between trapping in the regions where the ejection
rate of the environment vanishes and mixing due to its temporal dependence
leads to large fluctuations of mass. These mechanisms are found to result in
the presence of intermediate power-law tails in the probability distribution of
the mass density. For spatially differentiable environments, the exponent of
the right tail is shown to be universal and equal to -3/2. However, at small
values, it is found to depend on the environment. Finally, spatial scaling
properties of the mass distribution are investigated. The distribution of the
coarse-grained density is shown to posses some rescaling properties that depend
on the scale, the amplitude of the ejection rate, and the H\"older exponent of
the environment.
