The conclusion of "Desiree's Baby" is tragic: Desiree's child is dark-skinned, which implies that either she or her husband Armand have African ancestry. In the Antebellum South of the setting, to be part-black is a mark of shame. Armand, assuming Desiree is the one with black ancestry (since she was a foundling and no one knows who her biological parents are), essentially exiles her from his life.
Desiree is miserable and claims she wants to die if it turns out she is not fully white. Her adopted mother writes her a letter bidding her come back home with her child. After Armand makes it clear he wants Desiree gone, she takes her baby and walks to the bayou, still in her nightclothes.
Chopin makes it clear that Desiree is never seen again at Armand's estate, but the exact nature of her fate is unclear. Depending on the reader, one can assume she and her baby died in the bayou, or (less likely but still valid) she eventually reached Valmonde and lived there with her adopted parents in social exile.
When trying to rid every trace of Desiree from his estate, Armand ends up learning that he is the one who is part-black, as his mother was black. His pride and racism not only compelled him to drive away his wife and baby, but they have also left him humbled.