Was Wade Wilson a normal human (relatively speaking) before being experimented on by the Weapon X program? Did Weapon X give him his accelerated healing factor or simply awaken it? If so, and Weapon X did bring it to the surface, would that imply that Deadpool is in fact Inhuman?
If I'm not mistaken he was a normal human and that's why when he was diagnosed with cancer he couldn't do anything about it. We don't know that much about his past though, because even he himself cannot remember all of it due to his mental condition.
His healing ability was artificially given to him by the Weapon X and it was this that temporarily arrested his cancer (and could also cure other human diseases).
This ability is derived from Wolverine's.
Deadpool possesses a superhuman healing factor derived from that of the mutant Wolverine that allows him to regenerate damaged or destroyed areas of his cellular structure at a rate far greater than that of an ordinary human.
In the movie it says that the weapon X program "wakes up" mutant genes, and that either you mutate or die trying. This means that there are probably some people without these genes that die in the process of trying to mutate, and this suggests that Wade did have dormant mutant genes that were woken up after plenty of abuse.