In the canon series, the Diamonds are the most powerful gems in existence, being practically unstoppable when it comes to physical battles. They are revered by all gems under them as flawless beings inherently superior to them and all other lifeforms, much in the same way that humans tend to put gods and other idols on pedestals.
The powers of the Diamonds sounds a lot like the sort of things you would hear from gods of human religion, and they are only ever seen using their powers when provoked or when the universe has found an imbalance. Yellow Diamond possesses lightning powers and uses it on gems out of anger, much like a temperamental storm god. Blue Diamond can enforce her own negative emotions onto others, thus when she's miserable, everybody else is miserable. White Diamond can take away one's free will if it defies her own. All three of them and their empire has since lost their harmony when one of their own - Pink Diamond - has been displaced from the "natural order."
It can even be read in parallel to the theory that Yellow, Blue and Pink were split from White herself in a failed attempt to make herself a perfect being. Kami spirits would often be divided into separate, yet equal parts through a ritual ("Bunrei/Wakamitama") and one of those parts would be enshrined elsewere and would sometimes take on individual identities all their own (such as the case with the kami of Ōmiwa Shrine, who is an extension of Amaterasu-Ookami).
The gems in the comic are portrayed as yokai: demons and spirits that are more often than not formed from the stagnation, pollution and imbalance of human souls due to spiritual corruption. In-canon, most of the gems on Earth were corrupted into mindless beasts by the Diamonds as punishment for Pink's "death", and with many of the gems in the comic portrayed as yokai, it is possible that the existence of the yokai populating Japan was a direct cause of the kami due to the emotional imbalance caused by the death of a loved one "Pink" (or even just her absence in the cosmic order, leaving a vacuum of corruption), either having been inflicted (or eventually cured) by the kushi mitama.
With the reveal that Rose Quartz and Pink Diamond were the same person in-canon, this also means that Steven could be half-god, Rose having been rendered mortal due to being away from the Divine realm and her kin for too long and thus dying of childbirth, but her natural immortality allowing her disembodied soul to stay in mortal realm.
Given how her hair resembles a star and she has a tendency to glow, White Diamond with either be (or at least be an Expy of) Amaterasu-Ookami, Goddess of the Sun and the Universe, with Yellow, Blue and Pink being lesser (but still high-ranking) kami born from White's essence.