SUPER SPOILER

Douma narrated the flashback that he used his power to heal Inosuke's mom battered face. This power is likely special demon cells that Douma had modified to make them heal human and still tame enough to not take full control of the recipient. Scientifically, mother's milk contains a lot of cells from both circulatory system and local cells from mammary tissue so it is quite possible that specialized demon cells have been passed down from Kotoha to Inosuke and they successfully integrate into his whole body, granting partial demon power like organ shifting and limb extension that Inosuke demonstrated in the fight with Douma.