I would say its neither, or it changes. "doubt" in and of itself isn't a negative, but it seems to either function as a negative at times, or modify prhases and word groups into negatives. I'm not quite sure which.
You said "I doubt I will never see it", which means you think you will see it, as Perdweeb stated. Figure out the meanings of the un-italicized words, then the italicized words, and put them together, and you'll probably see it.