Generating diverse ideas requires being clear about the kind of input needed and creating multiple ways for diverse team members to share their ideas (e.g. use more than just a brainstorming session).
The very ability to empathize with a user requires that I have an understanding of that user's value and needs. This is what leads to many product fails. The individuals developing the innovation don't actually use it.
When you start paying attention to diversity, you notice it (and notice its absence!). And based on the culture of your upbringing and the culture of your organization, you may or may not be primed to think consciously about innovation.
Perspective taking is taking on the perspective of others. It's what we do anytime we buy a gift for someone else ("What would they like?"). So it means breaking the golden rule ("Treat others the way you want to be treated") and instead, acknowledges that others may not want what you want.