Daedric artifacts currently require Legendary Blacksmithing and an ordinary material perk, but most of them receive a tempering bonus from Daedric Smithing instead of the material perk. This is very inconsistent and doesn't make a lot of sense. Creating Daedric equipment by infusing Ebony with the essence of a slain Dremora doesn't teach to you how to improve the artifact of a Daedric Prince.
Divine artifacts should only require and benefit from Legendary Blacksmithing. From a gameplay perspective this implies standard Daedric gear still serves a purpose because it can be tempered better than Daedric artifacts.
Divine artifacts only require and benefit from Legendary Blacksmithing.
Artifacts that are not under the influence of a divine only require and benefit from the corresponding material perk.