Only patients with recurrent or progressive DIPG will be enrolled initially. Panobinostat will be administered every other day, 3 times/week, p.o. preferably on a Monday/Wednesday/Friday schedule for three weeks, followed by a rest period. Three weeks of therapy plus the one week rest period (total 4 weeks) will constitute one course. Treatment will continue for up to two years (26 courses) unless the patient experiences progressive disease, unacceptable toxicity or any of the off-study criteria.