They are not getting married, 'despite' rumors to the contrary. [=even though there have been rumors saying they are getting married]
The law has yet to be passed, 'despite the fact that' most people are in favor of it.
They grew to love each other, almost 'despite themselves'.
(..) Another... If anyone in here has any knowledge of Mr. Potter's movements this evening. I invite them to step forward. Now! It seems, despite your exhaustive defensive strategies, ... you still have a bit of security problem, Headmaster. I'm afraid it's quite extensive. (..)2011 Harry Potter and the Deathly Hallows: Part 2