I haven't finished Pokemon Sun and Moon yet but I'm quite interested in the concept of the Ultra Beasts. All of these Pokemon are quite different from what I've seen in previous Pokemon titles. And so, I took a bit reading on the Internet and seems people have various ideas about the concept of these Ultra Beasts so I also like to share those ideas and a bit of mine too.
According to the game then the Ultra Beasts are the "living creatures" come from outside the Earth (like the case of Deoxys). However, in Pokemon Sun and Moon they specifically call them as Ultra Beasts which come from the Ultra Space. I don't how the developers come up with this "Ultra Space" idea but one thing can be sured that they aren't originated from Earth and I don't even know whether they can be called as Pokemon or not (as there are no Poke-Ball on Earth can capture them). Although I haven't beaten Lusamine + Nihilego yet, what happened to Lusamine made me think that these guys can be extremely dangerous to Earth, or human in particular.
Most of the ideas on Internet suggest that the developer creates the Ultra Beasts based on the concept of 7 Deadly Sins and while there are no concrete information in-game. I believe this is quite a logic explaination. There are several ideas of what sin each beast may represent, but these are what I agree most:
1) UB01 Symbiont ・Nihilego ・Envy: Nihilego has ability to take shape of its desire target. It can also merge with other human, making Nihilego an ideal beast for the concept of Envy.
2) UB02 Absorbtion ・Buzzwole ・Pride: Buzzwole is a muscular beast with tremendous strength, he also seems to prefer posing, showing off its power. If that's true then it's worthy to be the embodiment of Pride.
3) UB02 Beauty ・Pheromosa ・Lust: Pheromosa has ability to allure all pokemons which encounters with it, leaving these pokemons unable to fight, a good idea as Lust.
4) UB03 Lightning ・Xurkitree ・Greed: I'm not really sure about this guy as Greed but according to wikia (if I remember right), this guy has an unending thirst for electricity. It often approaches power plant and drains all of its energy, then it will continue to another power plant. Kinda related to Greed at some point.
5) UB04 Blade ・Kartana ・Wrath: I can imagine why this guy is Wrath. I mean its entire body armed with blades, cutting everything on its wage and everything encounter it.
6) UB04 Blaster ・Celesteela ・Sloth: This colossal guy is quite a lazy guy by itself, as it stays still for most of the time.
7) UB05 Glutton ・Guzzlord ・Gluttony: Basically it eats everything on its path, just like the idea of Gluttony.
On my part, the first time I see these guys, especially Nihilego and Lusamine, it reminds me of the Lovecraftian Horror rather than 7 Deadly Sins (or it's because I don't think about it in the first place). According to Lovecraftian Horror stories then there are cosmic god-like beings who possess extreme knowledge and power which surpass human's capability. They can, and sometimes they will manipulate human community for their own plots. Some human also create cults worshipping these beings and often go insane (like the Cult of Cthulhu). Back to the case of Lusamine, it's quite similar at some point: Lusamine at first tried researching about Ultra Beast to get her husband back. But then gradually she went insane and being too obsessed with them.
Combining the two ideas, it seems Ultra Beasts is the concept from both 7 Deadly Sins and the Lovecraftian stories. Lovecraftian stories act as a foundation to create these Ultra Beasts, and the 7 Deadly Sins act as the way to define characteristics of each Ultra Beast. Personally I think this idea is quite neat. What do you think?
By the way, there is also question: can Ultra Beasts be considered as legendary pokemon? I seek answer from Internet and the answers quite vary. Many people said that they aren't since they are beings from Ultra Space and there are possiblity that there are tons of these out there. Other said that they are and I don't know where to start.
I'm also planning to write about the concept of new concept but I think that will need more research.
But anyway, thanks for reading this long post