Khalid Ramzi, a congregant, seemed to choke on the sermon. “We can’t fall into the same hole twice. We don’t want our children to be raised in violence and fear,” he said, standing outside the church in Irbil. “Only in our dreams can we go back to Mosul.”

When the militants swept into the city two years ago, Christians were ordered to convert, pay a tax or die. As the Islamic State pushed beyond the city, onto the plains of Nineveh, its advance scattered the rich patchwork of religious and ethnic minorities — Yazidis and Assyrians, Kurds and Shabaks — that made the area a microcosm of diverse Iraq and a place unlike perhaps any in the world.

Churches were torched. Yazidis were massacred or enslaved. Villages emptied as hundreds of thousands of people fled.

Iraqi forces advancing toward Mosul have recaptured some of the villages, raising the possibility of return for the minorities. But it is difficult to imagine the villages whole again, with their emptied streets and houses lying in ruin or despoiled by the militants.