  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.
