How do professors usually discover "new" research interests? Usually, a person starts out with a single primary research interest as a PhD student (closely related to that of their adviser). But then as they move on through the assistant professor stage, they discover new research interests. Do they usually discover new research interests through collaborations/discussions with professors at their university or through conferences? Or do they discover new research interests through what can earn them funding (through the NSF and other agencies?) Especially since any topic could theoretically be interesting to them? (even though they might find some topics more interesting than other topics).

Is it more often that they do what they're most interested in, or that they do what they obtain funding for (and find what they get funding for interesting enough)? And can they sometimes even discover new interests through their PhD students?
Here are a couple ways that have resulted in new research directions for me:


Reading a paper/book. Reading a paper/book can inspire new ideas. You may find that a paper is missing something, or you think of a way of doing it better, or perhaps you can combine the ideas in the paper with something you already know.
Obtaining funding. Often funding is obtained in groups, generally to inspire collaboration and cross-fertilization of ideas. As a result, one is forced to venture into new territory.
Talking to a colleague (generally from other institute). Simply chatting with someone at a conference or when visiting another institute can inspire new research directions. They may have a problem; you may have the tools to solve it.
Changing job. This brings you in contact with new people who have new problems. Collaborations my result from conversations in the coffee room, or by going to research discussions within the new department.
Following up on something a student has done. You may set a masters student, for example, to look at something you find interesting, but have not yet had time to explore in depth. The student may come up with something useful, but then leaves.