The sequence x_n = n^2 diverges to infinity: that is, it increases without bound.
Two roads diverged in a yellow wood, / And sorry I could not travel both /.
The sidewalk runs next to the street for a few miles, then diverges from it and turns north.
The software is pretty good, except for a few cases where its behavior diverges from user expectations.
Both stories start out the same way, but they diverge halfway through.