Using ab-initio non-Born-Oppenheimer simulations, we demonstrate
amplification of XUV radiation in a high-harmonic generation type process using
the example of the hydrogen molecular ion. A small fraction of the molecules is
pumped to a dissociative Rydberg state from which IR-assisted XUV amplification
is observed. We show that starting at sufficiently high IR driving field
intensities the ground state molecules become quasi-transparent for XUV
radiation, while due to stabilization gain from Rydberg states is maintained,
thus leading to lasing from strongly driven Rydberg states. Further increase of
the IR intensity even leads to gain by initially unexcited molecules, which are
quickly excited by the driving IR pulse
