  We discuss the single diffractive production of $c \bar c$ pairs and charmed
mesons at the LHC. In addition to standard collinear approach, for a first time
we propose a $k_t$-factorization approach to the diffractive processes. The
transverse momentum dependent (the unintegrated diffractive parton
distributions) in proton are obtained with the help of the Kimber-Martin-Ryskin
prescription where collinear diffractive PDFs are used as input. In this
calculation the transverse momentum of the pomeron is neglected with respect to
transverse momentum of partons entering the hard process. The results of the
new approach are compared with those of the standard collinear one.
Significantly larger cross sections are obtained in the $k_t$-factorization
approach where some part of higher-order effects is effectively included. Some
correlation observables, like azimuthal angle correlation between $c$ and $\bar
c$, and $c \bar c$ pair transverse momentum distribution were obtained for the
first time.
