The Abyss Demon
The Abyss Demon is a humanoid entity that resides in The Natural World. It has a classical demonic appearance with horns and texture like rocks.
The demon's presence may hint at the inaccessibility of glorious and pure things as the Father and Daughter and the Floating Castle in an impure human form, or perhaps the demon could symbolize the corruption of innocence.
Another speculation is the Castle and the happy Father and Daughter are idealizations and fantansies, for the reality of which a giant demon (symbolically representative of the size difference between that of an infant and an adult) stands between.
While walking across the bridge that leads to the Father and Daughter, it's possible for the Abyss Demon to appear and rise from below the bridge. He pops out and links you to Kyoto, and in some cases it will end the dream. He will also rise from the abyss when looking at the castle from a certain angle up close.