  We calculate the cross section for diffractive hadron production in deep
inelastic scattering off heavy nuclei in the framework of gluon
saturation/color glass condensate. We analyze the kinematic region of the
future Electron-Ion Collider. We argue that coherent and incoherent diffractive
channels are very sensitive to the structure of the nuclear matter at low $x$.
This expresses itself in a characteristic dependence of the cross sections on
rapidity and transverse momentum of the produced hadron and on the nuclear
weight. We also discuss dependence on the scattering angle and argue that both
coherent and incoherent cross sections may be within experimental reach at EIC.
