Coming from DianaMains, and with the understanding that this is an Aurelion vs Diana mid matchup.
This matchup HEAVILY favors Aurelion Sol from 1-5. Diana literally can only poke with Q, and if she does, she can't even CS without dancing to dodge stars and she won't be able to easily CS AND juke consistently.
As Diana, you need to simply not get pushed out and stay in XP range. Early laning consists of avoiding stars as best you can and watch to make sure he's not cornering you to land a Q into a few star procs. Farm at tower or whatever minions you can catch with Q; trying not to push at the same time. Being under Aurelion's tower as Diana pre-6 is asking to get camped. I suggest TP into this; a skilled Sol can push you out so often and so easily that sometimes your only real goal is to make it to 400-500 gold to back for a second Doring and TP back without dying.
That said, starting from level 4-5, look for opportunities to score CS AND land Q on him for poke. Try to limit the use of W, it's a mana hog. You do this leading up to level 6; your goal is to have Aurelion at around 55-65% while you're around the same or higher with AT LEAST 180 mana or more, preferably more of course.
Once you hit 6, he stands no chance against Diana, point blank. Unless he has a level, significant minion/item lead or has a lot of help, Aurelion is helpless against Diana. If you were able to poke him to around 60% while you're level 5, then you can kill him with ease at level 6 or later for the following reasons:
Both his Q and Ult have a slight cast time, a double tap of her Ult places her behind, meaning he needs to predict your Ult or whiff entirely. He is EXTREMELY squishy before RoA and Rylai, Diana is very tanky innately and her burst is a little on the ridiculous when even or ahead. At only 45 AP, her entire combo at level 6 inflicts around 500-550 damage; just over half what Sol will have at that level. Finally, she's ALL about getting in your face, and that's the last thing he wants.
I actually have begun running Protobelt against him for the simple fact that it lets me dash through his stars to initiate or juke both his Ult and Q with ease. But, if he's ahead or just plain dangerous, Abyssal first is good too. You can 100-0 with ease past Abyssal (assuming he is not ahead, as usual) but his skills mean his outplay potential is pretty big; one misstep and you eat a Q-ULT-handful of star procs. Shockingly, this is not enough to kill you assuming you took MR runes (health seals help), another point to Diana, but is enough to shove you out.
Teamfights are a different beast and they heavily rely on the teams comp, but Aurelion has the edge here with his powerful AoE damage and CC. If he loses sight of Diana though, or wastes a stun/knockback, she can dive him with impunity.