This phase II trial studies how well autologous stem cell transplant works in treating patients with favorable or intermediate risk, minimal residual disease (MRD)-negative, acute myeloid leukemia. Giving chemotherapy before a peripheral blood stem cell transplant helps kill any cancer cells that are in the body. After treatment, stem cells are collected from the patient's blood and stored. Higher dose chemotherapy is then given to prepare the bone marrow for the stem cell transplant. The stem cells are then returned to the patient to replace the blood-forming cells that were destroyed by the chemotherapy.