  We present cross sections for diphoton production in (semi)exclusive $PbPb$
collisions, relevant for the LHC. The calculation is based on equivalent photon
approximation in the impact parameter space. The cross sections for elementary
elastic scattering $\gamma \gamma \to \gamma \gamma$ subprocess are calculated
including two mechanisms: box diagrams with leptons and quarks in the loops and
a mechanism based on vector-meson dominance (VDM-Regge) model with virtual
intermediate vector-like excitations of the photons. We get measureable cross
sections in $PbPb$ collisions. We present many interesting differential
distributions which could be measured by the ALICE, CMS or ATLAS Collaborations
at the LHC. We study whether a separation of box and VDM-Regge contributions is
possible. We find that the cross section for elastic $\gamma \gamma$ scattering
could be measured in the heavy-ion collisions for subprocess energies smaller
than $W_{\gamma\gamma} \approx 15-20$~GeV.
