The Abyss Demon
The demon's presence may show inaccessibility to such glorious and pure things as the Father and Daughter and the Floating Castle as an impure human, or perhaps he symbolizes 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.