  The leading twist theory of nuclear shadowing predicts the shadowing
correction to nuclear parton distributions at small $x$ by connecting it to the
leading twist hard diffraction in electron-nucleon scattering. The
uncertainties of the predictions are related to the shadowing effects resulting
from the interaction of the hard probe with $N \ge 3$ nucleons. We argue that
the pattern of hard diffraction observed at HERA allows one to reduce these
uncertainties. We develop a new approach to the treatment of these multiple
interactions, which is based on the concept of the color fluctuations and
accounts for the presence of both point-like and hadron-like configurations in
the virtual photon wave function. Using the developed framework, we update our
predictions for the leading twist nuclear shadowing in nuclear parton
distributions of heavy nuclei at small $x$.
