  We use the Glauber-Gribov multiple scattering formalism and the theory of
leading twist nuclear shadowing to develop a method for the calculation of
leading twist hard coherent diffraction in hadron-nucleus processes. We
demonstrate that soft multiple rescatterings lead to the factorization breaking
of hard diffraction in proton-nucleus scattering, which is larger than in
hadron-nucleon scattering. At the LHC and RHIC kinematics, we compare the hard
diffractive to e.m.~mechanisms of hard coherent production of two jets in
proton-nucleus scattering. We study the x_{\Pomeron}, \beta and A-dependence of
the ratio of the dijet production cross sections due to the two effects, R. We
demonstrate that in proton-heavy nucleus hard coherent diffraction at the LHC,
R is small, which offers a clean method to study hard photon-proton scattering
at the energies exceeding the HERA energies by the factor of ten. On the other
hand, the use of lighter nuclei, such as Ca-40, will allow to study the
screened nuclear diffractive parton distribution. Moreover, a comparison of the
dijet diffractive production to the heavy-quark-jet diffractive production will
estimate the screened nuclear diffractive gluon PDF, which will be measured in
nucleus-nucleus ultraperipheral collisions at the LHC.
