  We discuss diffractive production of heavy mesons at the LHC. The
differential cross sections for single- and central-diffractive mechanisms for
$c\bar c$ pair production are calculated in the framework of the
Ingelman-Schlein model corrected for absorption effects. Here, leading-order
gluon-gluon fusion and quark-antiquark anihilation partonic subprocesses are
taken into consideration. Both pomeron flux factors as well as parton
distributions in the pomeron are taken from the H1 Collaboration analysis of
diffractive structure function and diffractive dijets at HERA. The extra
corrections from subleading reggeon exchanges are also taken into
consideration. In addition to standard collinear approach, for the first time
the differential cross sections for the diffractive $c\bar c$ pair production
are calculated in the framework of the $k_t$-factorization approach, i.e.
effectively including higher-order corrections. The unintegrated (transverse
momentum dependent) diffractive parton distributions in proton are calculated
with the help of the Kimber-Martin-Ryskin prescription where collinear
diffractive PDFs are used as input. Some correlation observables, like
azimuthal angle correlation between $c$ and $\bar c$, and $c \bar c$ pair
transverse momentum were obtained for the first time. The hadronization of
charm quarks is taken into account by means of fragmentation function
technique.
