Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study and for months after the last drug administration Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control while being treated on this study Patients of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while they are being treated on this study STRATUM A: Male participants of child fathering potential must be willing to use medically acceptable form of contraception during treatment and for weeks after stopping treatment STRATUM B: Male participants of child fathering potential must be willing to use medically acceptable form of contraception during treatment and for weeks after stopping treatment STRATUM C: Male participants of child fathering potential must be willing to use medically acceptable form of contraception during treatment and for months after stopping treatment Female patients of childbearing potential must have negative serum or urine pregnancy test within hours of the first dose of MEK; patient must not be pregnant or breast-feeding; patients of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study and for days following cessation of treatment Patients of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence during study treatment and months after the last dose of alisertib Males must agree to use a medically acceptable form of birth control in order to be in this study and for months after infusion Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study Females of childbearing age must be on an acceptable form of birth control per institutional standards Males who cannot comply with birth control use to avoid fathering a child Fertile male patients willing to use at least one medically acceptable form of birth control for the duration of the study and for weeks after treatment stops. Subjects of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study Subjects of childbearing potential requires acceptable form of birth control Patients of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study Fertile male subjects willing to use at least one medically acceptable form of birth control for the duration of the study and for weeks after treatment stops Non-menopausal or non-sterile female subjects of childbearing potential must have a negative serum beta-HCG and use a medically acceptable form of birth control RECURRENT/ PROGRESSIVE DIPG (STRATUM ): Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study and for months after the last dose of panobinostat NON-PROGRESSED DIPG (STRATUM ): Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study and for months after the last dose of panobinostat Patients of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study Subjects of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while they are being treated on this study (cohort ) Subjects of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while they are being treated on this study All patients of childbearing age must use an acceptable form of birth control All patients of childbearing and child-creating age must be using an acceptable form of birth control All patients of childbearing and child-creating age must be using an acceptable form of birth control Pregnancy, lactation or inability to use medically acceptable birth control if of childbearing potential