  A feasible mechanism of unitarization of amplitudes of deep inelastic
scattering at small values of Bjorken $x$ is the gluon fusion. However, its
efficiency depends crucially on the vacuum color screening effect which
accompanies the multiplication and the diffusion of BFKL gluons from small to
large distances. From the fits to lattice data on field strength correlators
the propagation length of perturbative gluons is $R_c\simeq 0.2-0.3$ fermi. The
probability to find a perturbative gluon with short propagation length at large
distances is suppressed exponentially. It changes the pattern of (dif)fusion
dramatically. The magnitude of the fusion effect appears to be controlled by
the new dimensionless parameter $\sim R_c^2/8B$, with the diffraction cone
slope $B$ standing for the characteristic size of the interaction region. It
should slowly $\propto 1/\ln Q^2$ decrease at large $Q^2$. Smallness of the
ratio $R_c^2/8B$ makes the non-linear effects rather weak even at lowest
Bjorken $x$ available at HERA. We report the results of our studies of the
non-linear BFKL equation which has been generalized to incorporate the running
coupling and the screening radius $R_c$ as the infrared regulator.
