Stacking attack speed on Diana makes her a pusher and gives her more tower threat, but less teamfight presence. Think of her as Master Yi in a sense when you stack attack speed. Her passive procs at a reduced rate to towers, but it still helps shred the towers health, and she actually downs a tower quite quickly with attack speed stacked.
Without the AP though, she becomes next to useless in late-game teamfights as she gets bursted down instantly (she's melee range) so she makes little use of her passive (One, maybe two procs). This damage can't make up for lost damage with AP burst plus the natural tankiness she can obtain from getting items like Rylai's, Zhonya's, and Abyssal Scepter.
I'm going to have to completely disagree with the comment on CDR being useless on her, though. It's probably the second most important stat to increase (first being AP obviously). Those QR procs are what make Diana so threatening, and dropping her Q from a 6 second CD to a 3.6 second CD dramatically increases her threat to the ADC and the team in general. In a focused teamfight with 400 AP, even one more Q adds 510 damage to each target before mitigation, realistically it'll be about 250 damage (to five champions this is 1250 damage). Adding another R this is another 225ish damage after mitigation. This is if she's focused down quickly. If she's left free reign on the teamfight it boosts her damage potential considerably.