So a couple of months back I was playing a game which was headed nicely towards a diplomatic victory, until the Ottomans finished conquering half the world's civs and declared on me, wiping out so many of the world's city states in the next few turns that diplo victory became essentially impossible.
I ended up switching to science production, and did manage to crank out an ultra-late science victory (this was on Immortal, and I'm amazed that nobody else had won by this point, it was so late, probably my highest turn count since I first started learning the game - I think everyone was too busy engaging in all war, all the time to bother actually winning).
Anyway, the only way I managed to survive this was by actually going for all the military techs that I never bother with and engaging in a massive protracted (sometimes nuclear) war until eventually half the world was nothing but dust and ash and the Ottomans stopped demanding all of my cities in exchange for peace. The AI never understands when it is getting utterly devastated, so I had all of my cities stacked with stealth bombers, GDRs all over the damn place, plus most of their cities gone before we managed to reach that point.
It was pretty fun, actually.