Atomic hydrogen is produced in xenon and krypton matrix by in situ x-ray induced photolysis of the dopants water, butane, acetone, or methane and trapped interstitially forming the "caged hydrogen" with characteristic VUV absorption bands. Their thermal bleaching as investigated between 8 K and 45 K cannot be described by a first-order process. A random walk model is introduced considering the hydrogen atoms to move in a thermally activated diffusive motion to traps where they become "invisible." The temperature dependence of the mean trapping time is Arrhenius-type and characteristic only for the matrix. Infrared experiments have confirmed a partial recovery of die dopant molecule only in krypton. Annealing-induced IR absorption bands are assigned to a new complex which involves two hydrogen atoms.