Inclusion Criteria:

        - ≥18 but ≤ 70 years of age

          -  Diagnosis of acute myeloid leukemia (AML) and meets one of the following disease
             criteria:

             * Primary induction failure:

             ** De Novo AML: no CR after 2, 3 or 4 induction attempts with high dose chemotherapy

               -  Secondary AML (from MDS or treatment related): no CR after 1, 2 or 3 cycles of
                  high dose chemotherapy

                    -  Relapsed:

               -  Not in CR after 1 or 2 cycles of standard re-induction therapy

               -  Relapse diagnosed at the time of the 6 months post-HCT standard of care follow-up
                  or later (i.e. based on bone marrow biopsy performed Day +170 or later) and
                  without evidence of graft versus host disease (GVHD)

                    -  For patients > 60 years of age, the minimum of 1 cycle of standard
                       chemotherapy is not required.

          -  Available HLA-matched or better but not fully HLA-matched (2/4 or 3/4 antigens)
             related donor (aged 18 to 75 years) with donor/recipient match based on a minimum of
             intermediate resolution DNA based Class I typing of the A and B locus who is CMV
             seropositive.

          -  Karnofsky Performance Status ≥ 60%

          -  Adequate organ function within 14 days of study registration (28 days for pulmonary
             and cardiac) defined as:

               -  Creatinine: Estimated glomerular filtration rate (eGFR) ≥ 50 mL/min/1.73m^2 per
                  current institutional calculation formula

               -  Hepatic: AST and ALT ≤ 3 x upper limit of institutional normal

               -  Pulmonary Function: oxygen saturation ≥ 90% on room air; PFT's required only if
                  symptomatic or prior known impairment - must have pulmonary function >50%
                  corrected DLCO and FEV1

               -  Cardiac Function: LVEF ≥ 40% by echocardiography or MUGA

               -  No symptomatic active conduction system abnormalities

          -  Able to be off prednisone or other immunosuppressive medications for at least 3 days
             prior to FATE-NK100 cell infusion (excluding preparative regimen premedications)

          -  Sexually active females of child bearing potential and males with partners of child
             bearing potential must agree to use effective contraception during therapy and for 4
             months after completion of therapy

          -  Voluntary written consent prior to the performance of any research related procedures

        Arm Specific Inclusion Criteria

        High-Risk aGVHD (ARM 1):

        - Pediatric or adult (ages 0-76 years) HCT recipients with high-risk acute GVHD, as
        determined either by the refined MN acute GVHD risk score [28]:
        http://z.umn.edu/MNAcuteGVHDRiskScore OR high risk on the basis of blood biomarkers (Ann
        Arbor Score 3) [31]. Patients in this arm must start treatment within the first 7 days
        after onset of high-risk aGVHD.

        or

        Steroid- Dependent aGVHD (ARM 2A):

        - Pediatric or adult (ages 0-76 years) HCT recipient with grade II-IV steroid-dependent
        acute GVHD, defined as any one of the following: Flare of acute GVHD of at least grade
        II/IV severity within 8 weeks of tapering down or (off of) immunosuppression for acute
        GVHD, with the flare occurring on ≤0.5 mg/kg prednisone. This can include late-onset aGVHD
        and overlap syndrome.

        or

        Steroid-Refractory aGVHD (ARM 2B):

        - Pediatric or adult (ages 0-76 years) HCT recipient with grade II-IV steroid refractory
        acute GVHD, defined as any one of the following:

          -  No response of acute GVHD after at least 4 days of systemic corticosteroids of at
             least 2 mg/kg prednisone or equivalent

          -  Progression of acute GVHD within 3 days of systemic corticosteroids of at least 2
             mg/kg prednisone or equivalent

          -  Failure to improve to at least grade II acute GVHD after 14 days of systemic
             corticosteroids, with initial doses of at least 2 mg/kg prednisone or equivalent

          -  Flare of acute GVHD of at least grade II/IV severity while on steroids at a dose
             >0.5/mg/kg/day. This can include late-onset aGVHD and overlap syndrome.

        Exclusion Criteria:

          -  Myocardial Infraction (MI) within the previous 6 months

          -  Acute leukemias of ambiguous lineage

          -  Pregnant or breastfeeding - The agents used in this study include those that fall
             under Pregnancy Category D - have known teratogenic potential. Women of child bearing
             potential must have a negative pregnancy test at screening

          -  History of or known active CNS involvement with AML

          -  Active autoimmune disease requiring systemic immunosuppressive therapy

          -  History of severe asthma and currently on chronic systemic medications (mild asthma
             requiring inhaled steroids only is eligible)

          -  New or progressive pulmonary infiltrates on screening chest X-ray or chest CT scan
             unless cleared for study by Pulmonary. Infiltrates attributed to infection must be
             stable/improving (with associated clinical improvement) after 1 week of appropriate
             therapy (4 weeks for presumed or documented fungal infections).

          -  Uncontrolled bacterial, fungal or viral infections including HIV-1/2 or active
             hepatitis C/B - chronic asymptomatic viral hepatitis is allowed

          -  Received any investigational agent within the 14 days before the start of study
             treatment (1st dose of fludarabine)