Inclusion Criteria:  Negative for SARS-CoV-2 infection as determined by an approved polymerase chain reaction (PCR) or an approved antigen test of any specimen Hospitalized with non-COVID-19-induced ARDS (any severity) with a PaO2/FiO2 (PF ratio) ≤ 300 Requires oxygen supplementation at Screening Willing to follow contraception guidelines  Exclusion Criteria:  Current standard of care treatments for ARDS appear to be working and the subject is clinically improving A previous stem cell infusion unrelated to this trial Pregnant or breast feeding or planning for either during the study Suspected uncontrolled active bacterial, fungal, viral, or other infection History of a splenectomy, lung transplant or lung lobectomy Concurrent participation in another clinical trial involving therapeutic interventions (observational study participation is acceptable) Expected survival or time to withdrawal of life-sustaining treatments expected to be < 7 days