  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. 
Diffractive processes at the LHC within $k_t$ -factorization approach