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'.
(..) ...the most logical delivery system for the terrorist to use... ...would be an airborne attack. A separate report has been filed... ...suggesting a train, despite the fact that the tunnels surrounding Parliament... ...have been sealed shut. Chief Inspector Finch. No, sir. Just a feeling. , (..)2005 V for Vendetta
(..) - We located the fireworks launch... ...and found traces of the explosives used at both sites. Unfortunately it appears that despite the heavy level of sophistication... ...these devices were homemade with over-the-counter chemicals... ...making them very difficult to trace. he's very good. (..)2005 V for Vendetta