DUHOK, Iraq—When Nisreen searches her baby’s budding features she can sometimes see traces of his father: the Islamic State militant who raped her, as his cohorts did to thousands of women from the Yazidi minority to which she belongs.

He was the third militant to take possession of Nisreen after she was captured in Iraq along with several thousand fellow Yazidis whom Islamic State targeted in a genocidal campaign in the summer of 2014.