This study is a multicenter, nonrandomized, open-label, dose-escalation with intra-patient dose-escalation, Phase 1 study of intravenous LY2523355 to determine the dose of LY2523355 that can be safely administered to patients with acute leukemia. Part A and Part B are dose escalation of two schedules in patients with acute leukemia. Parts A and B will enroll concurrently. Part C is a dose expansion for each schedule in patients with acute myeloblastic leukemia (AML).