Yumeria

Tomokazu Mikuri enters the dream world on his 16th birthday, witnessing a girl battling a giant floating creature. Upon waking, he finds the girl sleeping next to him. Mikuri soon discovers he can repeatedly enter the dream world, where he encounters more people he knows. There, he learns from a masked woman named Silk that they're fighting Faydoom, a being that grants powers to the girls to battle these monsters.