  Diffractive deeply virtual Compton scattering (DiDVCS) is the process
$\gamma^*(- Q^2) + N \rightarrow \rho^0 + \gamma^* (Q'^2)+ N'$, where N is a
nucleon or light nucleus, in the kinematical regime of large rapidity gap
between the $\rho^0$ and the final photon-nucleus system, and in the
generalized Bjorken regime where both photon virtualities $Q^2$ and $ Q'^2$ are
large. We show that this process has the unique virtue of combining the large
diffractive cross sections at high energy with the tomographic ability of
deeply virtual Compton scattering to scrutinize the quark and gluon content of
nucleons and light nuclei. Its study at an electron-ion collider would
enlighten the internal structure of hadrons.
