  Last year in [Phys. Rev. E 102, 042121 (2020)] the authors studied an
overdamped dynamics of nonequilibrium noise driven Brownian particle dwelling
in a spatially periodic potential and discovered a novel class of Brownian, yet
non-Gaussian diffusion. The mean square displacement of the particle grows
linearly with time and the probability density for the particle position is
Gaussian, however, the corresponding distribution for the increments is
non-Gaussian. The latter property induces the colossal enhancement of
diffusion, significantly exceeding the well known effect of giant diffusion.
Here we considerably extend the above predictions by investigating the
influence of nonequilibrium noise amplitude statistics on the colossal
Brownian, yet non-Gaussian diffusion. The tail of amplitude distribution
crucially impacts both the magnitude of diffusion amplification as well as
Gaussianity of the position and increments statistics. Our results carry
profound consequences for diffusive behaviour in nonequilibrium settings such
as living cells in which diffusion is a central transport mechanism.
