Safety Study of Human Myeloid Progenitor Cells (CLT-008) After Cord Blood Transplant for Hematologic Malignancy

Key Inclusion Criteria: * Undergoing allogeneic (4-6/6 matched) umbilical cord blood graft with at least 2.5 x 10e7 cells/kg for hematological malignancy: * High risk acute myeloid leukemia (AML) in complete remission * Very high risk pediatric AML; patients \<21 years eligible with \<25% blasts in marrow after failed chemotherapy * High risk acute lymphocytic leukemia (ALL) in complete remission * Chronic myelogenous leukemia (CML), excluding refractory blast crisis * Myelodysplasia (MDS) IPPS Int-2 or high risk, or refractory anemia with severe pancytopenia or high risk cytogenetics * Chronic lymphocytic leukemia (CLL), small lymphocytic lymphoma (SLL), marginal zone B-cell lymphoma or follicular lymphoma that have progressed after two prior therapies * Lymphoplasmacytic, lymphoma, mantle-cell lymphoma, prolymphocytic leukemia after initial therapy and complete or partial remission * Large cell non-Hodgkin lymphoma (NHL) in second complete or partial remission (chemotherapy refractory large cell NHL not eligible) * Lymphoblastic lymphoma, peripheral T cell lymphoma including angioimmunoblastic lymphoma, Burkitt's lymphoma, and other high-grade NHL after initial therapy if stage III/IV in complete or partial remission, or after progression if stage I/II \<1 year (chemotherapy refractory high-grade NHL not eligible) * Multiple myeloma beyond 2nd partial remission * Preparative regimen consisting of cyclophosphamide, fludarabine, and total body irradiation * Adequate organ function Key Exclusion Criteria: * Symptomatic underlying pulmonary disease or requiring oxygen * Active infection * HIV positive * Pregnant or nursing