I read a discussion on a blog about GG lore regarding who of the two made the first move - personally I have no idea but I'd say Ky is a bit more likely? (seeing just how shy Dizzy is most of the time)

With the bubble effects on this picture I am now ready to make a Shoujo manga

Edit: Fixed something about Dizzy's face that was bothering me

Guilty Gear is (c) Arc System Works