They key to fighting Diana isn't about trying to out trade her. It's about learning how her Cresent Strike works (her Q). It always goes out from her in a counter-clock wise motion and obviously it arcs.Try to get mechanically better at dodging her Q. It's not as easy of a skill to land once you learn how to counter act the skill shot.
Having better mobility is one way to do it. Kennen does well against her because Lightning Rush allows you to gain distance after she Rs in. --- Now playing: League Of Legends (FireAwayX), Guild Wars 2 (Floralei/Crownbird), World of Warcraft (shut up), SFxT (Poison/Nina, Juri/Lili)