  We evaluate the full current statistics (FCS) in the low dimensional (1D and
2D) diffusive conductors in the incoherent regime, $eV\gg E_{\rm Th}=D/L^2$,
$E_{\rm Th}$ being the Thouless energy. It is shown that Coulomb interaction
substantially enhances the probability of big current fluctuations for short
conductors with $E_{\rm Th}\gg1/\tau_E$, $\tau_E$ being the energy relaxation
time, leading to the exponential tails in the current distribution. The current
fluctuations are most strong for low temperatures, provided $E_{\rm Th}\sim
[(eV)^2/D\nu_1^2\bigr]^{1/3}$ for 1D and $E_{\rm Th}\sim (eV/g)\ln g$ for 2D,
where $g$ is a dimensionless conductance and $\nu_1$ is a 1D density of states.
The FCS in the "hot electron" regime is also discussed.
