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'.
(..) has any idea how he did it. This is all entirely useless. You are both grown men and, to the best of my knowledge, scientists. Please tell me that despite your enthusiasm for magic, you have discovered something of value that can help move this case forward. (..)2015 TvShow: Bones Title: The Promise in the Palace Season: 11 Episode 7