Can an invisible Higgs boson be seen via diffraction at the LHC?

We study the possibility of observing an `invisible' Higgs boson in central exclusive diffractive production at the LHC. We evaluate the cross section using, as a simple example, the Standard Model with a heavy fourth generation, where the invisible decay mode $H \to \nu_4 \bar{\nu}_4$ dominates, with the heavy neutrino mass $M(\nu_4) \simeq 50$ GeV. We discuss the possible requirements on trigger conditions and the background processes.