  In this contribution, we summarize NLO pQCD predictions for inclusive and
diffractive dijet photoproduction in Pb-Pb UPCs at the LHC. We demonstrate that
the theory describes well the preliminary ATLAS data on the inclusive cross
section, which probes nuclear parton distributions (PDFs) down to $x_A \approx
0.005$ and which can reduce current uncertainties of the small-$x$ nuclear
gluon distribution by approximately a factor of 2. Employing predictions of the
leading twist approach to nuclear shadowing for nuclear diffractive PDFs, we
calculate the cross section of diffractive dijet photoproduction and show that
its $x_{\gamma}$ dependence is sensitive to the effect of nuclear shadowing and
the mechanism of QCD factorization breaking in hard diffraction. We also find
that due to large leading twist nuclear shadowing and restricted kinematics,
the diffractive contribution to the inclusive cross section of dijet
photoproduction does not exceed $5-10$%, which helps with an ambiguous
interpretation of the ATLAS data.
