Curate, connect, and discover
Noctis would pick her up and carry her off to a safer location for her to calm down. He would then try to talk to her, bring up topics such as plants or animals. Then it's snack and nap time for them both.
Gladio wouldn't let anyone but Noct, Prompto and Ignis near her. He will even try to fight Nyx and Cor but it usually ends with Cor threatening to tell his father.
Prompto would sit next to Dia and just start chatting with her about anything. They can go from one topic that is small to a three hour discussion on why chocobos are the best thing.
Ignis would lead Dia to a more comfortable place and talk to her. Listening to her issue then think of a solution to help her. She feels safer around him and would usually grasp his sleeve when she feels depressed.
Cor would stand by her and wait until her attack was done. The last time he left her alone during an episode she ended up in the hospital trying to kill herself. He's known about her problems since Nyx brought her in and he doesn't want her to suffer fully. When she's done he will talk to her and tell her that the future holds a better life if she stays by his side. He is a father figure to her anyway.