  We consider single-diffractive (SD) Higgs production in association with
heavy flavour in proton-proton collisions at the LHC. The main focus of our
study is a reliable estimate of SD/inclusive ratio, not a precision computation
of the cross sections. The calculations are performed within the framework of
the phenomenological dipole approach, which includes by default the absorptive
corrections, i.e. the gap survival effects at the amplitude level. The dominant
mechanism is the diffractive production of heavy quarks, which radiate a Higgs
boson (Higgsstrahlung). Although diffractive production of $t$-quarks is
grossly suppressed as $1/m_t^2$, the large Higgs-top coupling compensates this
smallness and the Higgsstrahlung by $t$-quarks becomes the dominant
contribution at large Higgs boson transverse momenta. We computed the basic
observables such as the transverse momentum and rapidity distributions of the
diffractively produced Higgs boson in association with the bottom and top quark
pair. Finally, we discuss a potential relevance of the diffractive
Higgsstrahlung in comparison to the Higgsstrahlung off intrinsic heavy flavor
at forward Higgs boson rapidities.
