  We extend the theory of leading twist nuclear shadowing to calculate leading
twist nuclear diffractive parton distribution functions (nDPDFs). We observe
that the quark and gluon nPDFs have different patterns of the $A$-dependence.
  It is found that the probability of diffraction in the quark channel
increases with $A$, reaching about 30% at $x \sim 10^{-4}$ for $A \sim 200$,
and weakly decreases with $Q^2$. In the gluon channel, the probability of
diffraction is large for all nuclei ($\sim 40$% for heavy nuclei at $x \sim
10^{-4}$ and $Q_0^2 \sim 4$ GeV$^2$), it weakly depends on $A$ and it decreases
rather fast with increasing $Q^2$ -- the probability decreases by approximately
a factor of two as $Q^2$ changes from 4 GeV$^2$ to 100 GeV$^2$. We also find
that nuclear shadowing breaks down Regge factorization of nDPDFs, which is
satisfied experimentally in the nucleon case. All these novel effects in nDPDFs
are large enough to be straightforwardly measured in ultraperipheral collisions
at the LHC.
