The primary objectives of the study are to (1) describe the toxicity profile and define the dose-limiting toxicities of panobinostat in children with recurrent/progressive DIPG, or with non-progressed DIPG taken every other week; (2) estimate the maximum tolerated dose and/or the recommended Phase 2 dose of panobinostat in children with recurrent/progressive DIPG, or with non-progressed DIPG taken every other week; and (3) evaluate and characterize the plasma pharmacokinetics of panobinostat in children with recurrent/progressive DIPG, or with non-progressed DIPG taken every other week.