Kitsunegamis call "The Dream" the time they spent passing through the portal. During that time each Kitsunegami knew a divine entity who helps him/her to release the bad feelings. During this, the Kitsunegami remembers something utterly special for him/her, and the unknown divine entity uses that memory to transform the Kitsunegami (giving him/her a new appearance). Finally, the Kitsunegami is sent to the new world.
The Kitsunegamis have been wondering what that divine entity (or divine entities) could be. It looks like it's different from one Kitsunegami to another. However, they don't know how to learn more about it, there hasn't been any contact since awakening The Dream.
You can read a little comic about it:
