The model of Kangi-ten is Ganesha, a deity of Hinduism.
Originally, Ganesha was a greedy devil who had an elephant head on a human body, making people suffer from plague.
Kannon, the Goddess of Mercy, was distressed at Ganesha's violence. So Kannon transformed into a figure of woman devil and suggested to Ganesha she quench his sexual lust, in exchange for him to become a believer in Buddhism.
Ganesha was delighted to accept the proposal and became Kangi-ten, one of guardian deities of Buddhism.
That is why Kangi-ten has two elephant heads on two human bodies hugging each other. "Kangi" means great ecstasy.