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.

The resolution of a story takes place after the climax. It is the part of the story where the conflict comes to an end. In Kate Chopin's "Désirée's Baby," the resolution comes after Désirée and her baby leave the plantation. 

She disappeared among the reeds and willows that grew thick along the banks of the deep, sluggish bayou; and she did not come back again.

Weeks after her disappearance, Armand orders his slaves to put up a huge fire. In it, he burns all of the things that used to belong to Désirée and the baby. There were also letters thrown in the fire, some from Désirée, and others from Armand's own mother. Chopin ends the story by citing the writing on the letter, in which Armand's mother states that she is very grateful to God for her husband's love. However, she was even more grateful for the fact that Armand will never have to find out that she, his mother, is African American. 

This is significant because the entire reason Désirée leaves Armand is because their baby has developed African American physical traits. These were the days before the Civil War, and slavery was in full swing. That the baby was black meant that either Armand or Désirée was also of the same descent. Armand, who is a cruel and difficult man, automatically blames Désirée for it and insists that she is the one who carries this heritage—that it is her fault that their child is of "the race that is cursed with the brand of slavery."

In total despair, Désirée leaves the plantation, presumably to go see her mother. What she does, however, is drown herself and the baby in the bayou.

Therefore, the resolution is tragic and ironic because it is now clear that Armand is the one who carries the African American genes in his blood, from his mother, and he has just caused the unnecessary and cruel deaths of his wife and child.

The fire that Armand built was intended to burn Desiree's belongings and her child's. Fire, as s symbol of rebirth and destruction is also the element that disconects Armand from his present situation. However, we know that Armand also burned a letter which stated that he, himself, was part black. In this burning, he is also disconecting himself from his past, his present, and his future. He was basically doing everything in his power to burn the truth, and pretend that nothing ever was.

In order to answer this question, you first need to identify the conflict (or the problem) of the story. Though a very short short-story, "Desiree's Baby" presents more than just one simple conflict.

First, there is the mystery of the identity of Desiree, and of course, her partially black baby. Is there a slave in the ancestry of the baby's mother or father? This is the first problem.

Of course, Armand suggests and fully acts upon the assumption that Desiree must be the one who has brought slave ancestry into his family line, and rejects his son and his wife as a result. This creates the external conflict between Desiree and her husband, which outside of her leaving and returning to the home of her parents, goes otherwise unresolved. The only thing the audience knows of the "resolution" of this conflict is:

She disappeared among the reeds and willows that grew thick along the banks of the deep, sluggish bayou; and she did not come back again.

Though Armand "solves" his personal conflict, the bigger picture remains untold, as we never hear of Desiree again.

The mystery of identity, the primary conflict, is somewhat resolved in the final line of the story:

...our dear Armand will never know that his mother, who adores him, belongs to the race that is cursed with the brand of slavery.

The resolution comes in the form of showing the audience that Armand was wrong. However, the big picture ends in ambiguous irony. Chopin purposefully ends her story on an ironic surprise ending and leaves lose ends untied, most likely, to cause her audience to draw its own conclusions. It is clear the focus here is not on solving the conflict between the two main characters or even within Armand himself. Instead, the purpose seems to be to draw attention to a third, and more global conflict, which is that of the human condition and its propensity toward prejudice, hatred, and superiority.

Chopin is showing that a societal conflict exists in the context of the story, and does not present a resolution, likely because at the time she wrote the story, one did not exist. Some might argue that the conflict of human hatred and prejudice is one that will never be fully resolved.