Sorafenib in Combination With Cytarabine and Clofarabine in Patients With Refractory or Relapsed Hematologic Malignancies

Inclusion Criteria: * Patients must have a diagnosis of acute myeloid leukemia (AML), acute promyelocytic leukemia (APL), acute lymphoblastic leukemia (ALL), infantile leukemia (either AML or ALL), AML with prior myelodysplastic syndrome (MDS), myelodysplastic/myeloproliferative neoplasms, or biphenotypic leukemia. Patients with treatment-related AML (t-AML) will be eligible, provided they meet all other eligibility criteria. * Current disease status must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life. Patients must meet one of the following criteria: 1. First or greater relapse, 2. Refractory to 1 or more courses of induction or reinduction chemotherapy, or 3. First or greater relapse after allogeneic hematopoietic stem cell transplantation (HSCT). * Age: participants must be \< 31 years of age at the time of study entry. St. Jude participants will include the following: * Participants currently on therapy at St. Jude, or within 3 years of completing therapy at St. Jude must be ≤ 24 years of age. * Other participants must be ≤ 21 years of age. Performance status: Karnofsky \>50% for ≥ 16 years of age; Lansky \>50% for children \<16 years of age. Organ Function Requirements: 1. Hepatic: * Serum direct bilirubin ≤2.0 mg/dl. * Alanine transaminase (ALT/SGPT) ≤4 x ULN 2. Cardiovascular: • Shortening fraction of greater than or equal to 25% by echocardiogram 3. Pulmonary: • Pulse oximetry ≥93% at room air 4. Renal: • Creatinine clearance or radioisotope GFR greater than or equal to 70 mL/min/1.73m2 or serum creatinine based on age 5. Pancreas: * Amylase and lipase ≤ 2 × upper limits of normal Participant or legal guardian, in the opinion of the investigator, is capable of understanding the investigational nature, potential risks and benefits of the study, and able to provide valid informed consent. A signed informed consent must be obtained prior to any study specific procedures. Exclusion Criteria: * Participants who have relapsed while on sorafenib therapy. * Uncontrolled hypertension, defined below: * Patients \< 18 years old: * Diastolic Blood Pressure Within The Upper Limit Of Normal Defined as: A diastolic blood pressure (DBP) \> the 95th percentile for age and gender despite optimal medical management. * Patients ≥ 18 years old * Uncontrolled hypertension defined as systolic blood pressure \> 150 mmHg or diastolic pressure \> 90 mmHg despite optimal medical management. . * Use of concomitant chemotherapy, investigational agents, radiation therapy, or immunotherapy other than as specified in the protocol. * Use of investigational agents within 30 days or any anticancer therapy within 2 weeks before study entry with the exception of hydroxyurea, low dose cytarabine and intrathecal chemotherapy. * Any other severe concurrent disease, or have a history of serious organ dysfunction or disease involving the heart, kidney, liver, or other organ system that may place the participant at undue risk to undergo treatment. * Participant with a systemic fungal, bacterial, viral or other infection not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement), despite appropriate antibiotics or other treatment). * Any significant concurrent disease, illness, or psychiatric disorder that would compromise participant safety or compliance, interfere with consent, study participation, follow-up, or interpretation of study results. * Participants must not receive concomitant medications known to inhibit platelet function or known to selectively inhibit cyclooxygenase-2 (COX-2) activity (i.e., all antipyretic and anti-inflammatory medications except acetaminophen). * There is no available information, as yet, regarding human fetal or teratogenic toxicities. Pregnancy tests with a negative result must be obtained in girls who are postmenarchal within 10 days before start of treatment. Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation. Men and women should use adequate birth control for at least three months after the last administration of study treatment. * Pregnant or lactating. * Known human immunodeficiency virus (HIV) infection. * Thrombolic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months * Cardiac disease: Congestive heart failure \> class II NYHA. Patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * Pulmonary hemorrhage/bleeding event \> CTCAE Grade 2 within 4 weeks of first dose of study drug. * Any other hemorrhage/bleeding event \> CTCAE Grade 3 within 4 weeks of first dose of study drug * Serious non-healing wound, ulcer, or bone fracture. * Evidence or history of bleeding diathesis or coagulopathy. * Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug. * Concomitant use of St. John's Wort or rifampin (rifampicin) * Known or suspected allergy to any agent given in the course of this trial. * Any malabsorption problem. * Have had a diagnosis of another malignancy, unless the participant has been disease-free for at least 3 years following the completion of curative intent therapy with the following exceptions: * Participants with treated non-melanoma skin cancer, in situ, carcinoma, or cervical intraepithelial neoplasia, regardless of the disease-free duration, are eligible for this study if definitive treatment for the condition has been completed. * Patients with organ-confined prostate cancer with no evidence of recurrent or progressive disease based on prostate-specific antigen (PSA) values are also eligible for this study if hormonal therapy has been initiated or a radical prostatectomy has been performed. * Participants who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study. * Inability or unwillingness of research participant or legal guardian or representative to give written informed consent.