Single Treatment With FT1050 of an Ex-vivo Modulated Umbilical Cord Blood Unit

Inclusion Criteria: 1. Subjects with hematologic malignancies for whom allogeneic stem cell transplantation is deemed clinically appropriate. Eligible diseases and stages include: * Non-Hodgkin's lymphoma or Hodgkin's lymphoma * Chronic lymphocytic leukemia (CLL) * Acute myelogenous leukemia (AML) * Chronic myelogenous leukemia (CML) 2. Lack of 5-6/6 HLA-matched related or 8/8 HLA-A, B, C, DRß1 matched unrelated donor; or unrelated donor not available within appropriate timeframe. * Identification of suitable backup CB unit(s) (single unit with pre-cryopreservation cell dose ≥ 2.5 x 10\^7 TNC/kg or two units with pre-cryopreservation cell dose ≥ 1.5 x 10\^7 TNC/kg each) and meeting minimum HLA match criteria. * An acceptable alternative to one or two backup CB unit(s) is the identification of an eligible related haploidentical donor that meets minimum HLA match criteria. 3. Age 18-65 years. 4. Eastern Cooperative Oncology Group (ECOG) performance status 0-2. 5. Signed IRB approved Informed Consent Form (ICF). Exclusion Criteria: 1. The following hematologic malignancies are excluded: * Myelofibrosis (Agnogenic Myeloid Metaplasia) * Aplastic anemia. 2. Previous treatment that included an allogeneic transplant 3. Cardiac disease: symptomatic congestive heart failure or evidence of left ventricular 4. dysfunction (Ejection fraction \< 40%) as measured by gated radionucleotide ventriculogram or echocardiogram; active angina pectoris, or uncontrolled hypertension; history of myocardial infarction with depressed ejection fraction. 5. Pulmonary disease: symptomatic chronic obstructive lung disease, symptomatic restrictive lung disease, or corrected DLCO of \< 50% of predicted, corrected for hemoglobin. 6. Renal disease: serum creatinine \> 2.0 mg/dl and calculated creatinine clearance \< 40 mL/min 7. Hepatic disease: serum bilirubin \> 2.0 mg/dl (except in the case of Gilbert's syndrome or ongoing hemolytic anemia), SGOT or SGPT \> 3 x upper limit of normal. 8. Neurologic disease: symptomatic leukoencephalopathy, active CNS malignancy or other neuropsychiatric abnormalities believed to preclude transplantation. 9. HIV antibody. 10. Uncontrolled infection. 11. Pregnancy or breast feeding mother. 12. Inability to comply with the requirements for care after allogeneic stem cell transplantation. 13. Participation in a concurrent clinical trial with a novel, unapproved investigational agent \< 30 days prior to Day 0.