Clofarabine, Cytarabine, and Filgrastim Followed by Infusion of Non-HLA Matched Ex Vivo Expanded Cord Blood Progenitors in Treating Patients With Acute Myeloid Leukemia

Inclusion Criteria

• •Cohort A: Diagnosis of AML by World Health Organization (WHO) criteria, either relapsed or refractory; acute promyelocytic leukemia \[Acute promyelocytic leukemia with t(15;17)(q22;q12) and variants\] will be eligible only after failure of a regimen containing arsenic trioxide; patients in this cohort must have had an initial remission duration of \< 1 year and cannot have received any prior salvage chemotherapy
• •Cohort B: Untreated AML patients, excluding those with favorable cytogenetic or molecular abnormalities per the European LeukemiaNet recommendations
• •Cohort C: Untreated AML patients, including those with favorable cytogenetic or molecular abnormalities per the European LeukemiaNet recommendations
• •The first three patients enrolled in cohorts A and B must be less than 60 years old; thereafter, patients aged \>= 18 and =\< 70 are eligible
• •The first three patients enrolled in cohorts A and B must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 -1; thereafter, ECOG performance status of 0-2 is required
• •Serum creatinine =\< 1.0 mg/dL; if serum creatinine \> 1.0 mg/dl, then the estimated glomerular filtration rate (GFR) must be \> 60 mL/min/1.73 m\^2 as calculated by the Modification of Diet in Renal Disease equation where predicted GFR (ml/min/1.73 m\^2) = 186 X (Serum Creatinine)\^-1.154 X (age in years)\^-0.203 X (0.742 if patient is female) X (1.212 if patient is black)
• •Serum total bilirubin =\< 1.5 x upper limit of normal (ULN) unless elevation is thought to be due to Gilbert's syndrome, hemolysis, or hepatic infiltration by the hematologic malignancy
• •Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 X ULN, unless elevation is thought to be due to hepatic infiltration by the hematologic malignancy
• •Alkaline phosphatase =\< 2.5 x ULN
• •Capable of understanding the investigational nature, potential risks and benefits of the study, and able to provide valid informed consent
• •Female patients of childbearing potential must have a negative serum pregnancy test within 2 weeks prior to enrollment
• •Male and female patients must be willing to use an effective contraceptive method during the study and for a minimum of 90 days after study treatment