  Gluon amplitudes at most-subleading order in the $1/N$ expansion share a
remarkable simplicity with graviton amplitudes: collinear divergences are
completely absent in both and, as a consequence, their full IR behavior arises
from soft gluon/graviton exchange among the external states. In this paper we
study the effect of all-loop IR divergences of celestial most-subleading color
gluon amplitudes and their similarities with the celestial gravity case. In
particular, a simple celestial exponentiation formula for the dipole part can
be written. We also analize how this exponentiation is modified by non-dipole
contributions. Finally we also show that, in the Regge limit, the soft factor
satisfies the Knizhnik-Zamolodchikov equation hinting at the possibility that,
in this limit, an effective Wess-Zumino-Witten model would describe the
dynamics of the infrared sector.
