This phase I trial studies the side effects and best dose of panobinostat in treating younger patients with diffuse intrinsic pontine glioma (DIPG). Panobinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Stratum 1 treats patients with DIPG that has returned or gotten worse (progressed). Stratum 2 treats patients with DIPG that has not yet gotten worse. Currently, only Stratum 2 is enrolling patients.