Higgs production within $k_t$-factorization with unintegrated gluon distributions

We present differential cross sections for Higgs boson and/or two-photon production from intermediate (virtual) Higgs boson within the formalism of $k_t$-factorization. Resulting distributions for two photons from the Higgs boson are compared with recent ATLAS collaboration data. In contrast to a recent calculation the leading order $g g \to H$ contribution is rather small compared to the ATLAS experimental data ($\gamma \gamma$ transverse momentum and rapidity distributions). We include also higher-order contribution $g g \to H (\to \gamma \gamma) g$, $g g \to g H g$ and the contribution of the $W^+ W^-$ and $Z^0 Z^0$ exchanges. The $gg\to Hg$ mechanism gives a similar contribution as the $gg\to H$ mechanism. We argue that there is almost no double counting when adding $gg\to H$ and $gg\to Hg$ contributions due to different topology of corresponding Feynman diagrams. The final sum is comparable with the ATLAS two-photon data.