Louise imagined Cheese, but he is known to often get out. In Mac Daddy, Cheese enters Mac's room and when Mac wakes up, Cheese appears in his bed, leading Mac to believe that he had created Cheese. Towards the end of that same episode, Mac finds out that Louise had created Cheese and she had explained that Cheese occasionally wanders off.
In Cheese a Go-Go, Frankie brings Cheese back to Louise's apartment after a long day of chasing him around town. When Frankie asks where Cheese had to go, Louise simply exclaimed that Cheese just "had to go."
In Goodbye to Bloo, Mac claims that Louise and her family are moving into another apartment, specifically one that has a "no pets or imaginary friends" rule. This means that Louise has to give up her imaginary friend, Cheese, and that Cheese has to live at Foster's, much to everyone's horror.