Inclusion Criteria:

          1. Male or female subjects ≤ 21 years-of-age with the demonstrated ability to swallow
             capsules whole and who are willing to provide access to previously obtained biopsy
             results

          2. Provision of written informed consent and assent, when applicable, for tumor
             resection, stereotactic surgery, tumor biopsy, sample collection, and/or treatment
             with study drug prior to undergoing any study-specific procedures

          3. Arm 1: Evidence of recurrent or progressive supratentorial tumor, which has shown a >
             25% increase in bi dimensional measurements by MRI or is refractory with significant
             neuro deterioration that is not otherwise explained with no known curative therapy,
             not in direct continuity with the ventricular system (e.g., there is physical
             separation between the tumor and ventricle, the tumor does not open directly into the
             ventricular system).

             Arm 2: Clinical presentation of DIPG and compatible MRI with approximately 2/3 of the
             pons included and without evidence of dissemination. Subjects should be ≥ 2 weeks and
             ≤ 10 weeks post standard focal radiotherapy (ie, dose of 5400 to 5960 cGy and maximum
             dexamethasone of 1 mg/m2/day)

          4. At the time of registration, subjects must have recovered from the toxic effects of
             previous treatments, as determined by the treating physician.

               1. Targeted agents, including small-molecular tyrosine kinase inhibitors: 2 weeks

               2. Other cytotoxic agents: 3 weeks

               3. Nitrosoureas: 6 weeks

               4. Monoclonal antibody immunotherapies (eg, PD-1, CTLA-4): 6 weeks

               5. Vaccine-based and/or viral therapy: 3 months

          5. On a stable or decreasing dose of dexamethasone for the previous 7 days

          6. Able to undergo standard MRI scans with contrast agent before enrollment and after
             treatment

          7. Have age-appropriate functional performance:

               1. Lansky score ≥ 40 or

               2. Karnofsky score > 50 or

               3. Eastern Cooperative Oncology Group (ECOG) score ≤ 2

          8. Have adequate bone marrow reserves and liver and kidney function, as assessed by the
             following laboratory requirements:

               1. Hemoglobin ≥ 8 g/L

               2. Absolute lymphocyte count ≥ 500/mm3

               3. Absolute neutrophil count ≥ 1000/mm3

               4. Platelets ≥ 100,000/mm3 (untransfused [> 5 days] without growth factors)

               5. Serum creatinine ≤ 1.5 x upper limit of normal (ULN) for age

               6. Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 x ULN for age

               7. Total bilirubin < 1.5 x ULN for age

               8. International normalized ratio (INR) and activated thromboplastin time within
                  normal institutional limits

          9. Male and female subjects of childbearing potential must agree to use a highly reliable
             method of birth control (expected failure rate < 1% per year) from the Screening visit
             through 28 days after the last dose of study drug. Women of childbearing potential
             must have a negative pregnancy test at screening.

        Exclusion Criteria:

          1. Radiotherapy treatment prior to the first veledimex dose:

               1. Focal radiation ≤ 4 weeks

               2. Whole-brain radiation ≤ 6 weeks

               3. Cranio-spinal radiation ≤ 12 weeks NOTE: Subjects in Arm 2 (ie, with DIPG) must
                  be ≥ 2 weeks and ≤ 10 weeks after standard focal radiotherapy (dose of 5400 to
                  5960 cGy and maximum dexamethasone of 1 mg/m2/day)

          2. Subjects with clinically significant increased intracranial pressure (eg, impending
             herniation or requirement for immediate palliative treatment) or uncontrolled seizures

          3. Subjects whose body surface area (BSA) would expose them to < 75% or > 125% of the
             target dose

          4. Known immunosuppressive disease, autoimmune condition, and/or chronic viral infection
             (eg, human immunodeficiency virus [HIV], hepatitis)

          5. Use of systemic antibacterial, antifungal, or antiviral medications for the treatment
             of acute clinically significant infection within 2 weeks of first veledimex dose.
             Concomitant therapy for chronic infections is not allowed. Subjects must be afebrile
             prior to Ad-RTS-hIL-12 injection; only prophylactic antibiotic use is allowed
             perioperatively

          6. Use of enzyme-inducing antiepileptic drugs (EIAEDs) within 7 days prior to the first
             dose of study drug

          7. Other concurrent clinically active malignant disease, requiring treatment

          8. Nursing or pregnant females

          9. Prior exposure to veledimex

         10. Use of medications that induce, inhibit, or are substrates of cytochrome p450 (CYP450)
             3A4 within 7 days prior to veledimex

         11. Use of heparin or acetylsalicylic acid (ASA). The use of systemic heparinization, or
             any ASA containing medications, is prohibited during active dosing with veledimex.
             Prophylactic heparin SC, per institutional protocol, or heparin when used for
             maintaining patency of an access port of a PICC line is permitted.

         12. Presence of any contraindication for a neurosurgical procedure

         13. Unstable or clinically significant concurrent medical condition that would jeopardize
             the safety of a subject and/or their compliance with the protocol