  We demonstrate that hard dijet production via coherent inelastic diffraction
is a promising channel for probing gluon saturation at the Electron-Ion
Collider. By $inelastic$ diffraction we mean a process in which the two hard
jets - a quark-antiquark pair generated by the decay of the virtual photon -
are accompanied by a softer gluon jet, emitted by the quark or the antiquark.
This process can be described as the elastic scattering of an effective
gluon-gluon dipole. The cross section takes a factorised form, between a hard
factor and a unintegrated ("Pomeron") gluon distribution describing the
transverse momentum imbalance between the hard dijets. The dominant
contribution comes from the black disk limit and leads to a dijet imbalance of
the order of the target saturation momentum $Q_s$ evaluated at the rapidity
gap. Integrating out the dijet imbalance, we obtain a collinear factorization
where the initial condition for the DGLAP evolution is set by gluon saturation.
