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 Contras feel they must be outnumbered That's a given They've managed to hold their ground despite the fact that their weapons have been acting up No new shipment of arms is expected until tomorrow (..)1987 Broadcast News