Regeneration is the supernatural ability possessed by Hybrids, Surgos, and Phoenixes to magically heal and regenerate bodily tissue and organs damaged as a result of injuries. This regeneration takes place quickly usually within seconds depending on the injury. The ability is also powerful enough to revive the possessor even after otherwise fatal injuries and wounds such as snapped necks, burns, broken bones, and gun shots. However, most beings cannot be regenerate after heart extraction or decapitation.
Hybrids have the ability to automatically heal from injuries and wounds in seconds, stemming from their parent's reconstitution. It is a weaker version of this ability, but it has been shown to be very useful, allowing them to bounce back from snapped necks and gunshot wounds. These are non-fatal, but things such as decapitation, heart extraction, and limb removal cannot be healed as the body cannot is not together anymore.
A Phoenix possesses the greatest aspect of this ability, almost indestructible due to their destiny of longevity. Their regeneration is amplified, allowing them to recover from injuries extremely fatal. Jules has shown this throughout the series. Her greatest accomplishment was being able to survive and immediately heal from an explosion, walking out easily. This would've killed any other being, supernatural or human. She noted that her body was healing faster than injuries, allowing her to stay in one piece. Their ashes have been said to contain healing factors as well.
Surgos also posses the ability to healing automatically. However, when great power is applied, they will be killed without being able to regenerate. Their bodies need to be dismembered, burned, and buried, however before their power of reconstitution kicks in.