A Study to Evaluate the Safety and Efficacy of Nivolumab Monotherapy and Nivolumab in Combination With Ipilimumab in Pediatric Participants With High Grade Primary Central Nervous System (CNS) Malignancies

Inclusion Criteria: * Must have received standard of care therapy, and there must be no potentially-curative treatment available, in one of the following cohorts: * A newly diagnosed Diffuse Intrinsic Pontine Glioma (DIPG) that has been treated with radiation therapy (RT) but no chemotherapy * A histologically confirmed recurrent or progressive non-brainstem High Grade Glioma (HGG) previously treated with surgical resection and RT * A histologically confirmed medulloblastoma that has relapsed or is resistant to at least one line of prior therapy including surgery, RT, and chemotherapy * A histologically confirmed ependymoma that has relapsed or is resistant to at least one line of prior therapy including surgical resection and RT * A histologically-confirmed high grade CNS malignancy "other than above" which is recurrent or progressive after at least one line of prior therapy * Lansky play score (LPS) for ≤ 16 years of age or Karnofsky performance scale (KPS) for \> 16 years of age assessed within two weeks of enrollment must be \>= 60 * A tumor sample must be available for submission to central laboratory (not required for DIPG) Exclusion Criteria: * An active, known, or suspected autoimmune disease * A concurrent condition requiring systemic treatment with either corticosteroids or other immunosuppressive medications within 14 days of start of study treatment * Known history of positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndro…