7ft.
If I jump off the top of my rock waterfall and do a cannonball, my bum hits the bottom of the pool. Not hard, mind you, as the water is enough to slow me down, but diving is dangerous in a pool that's not designed for it even if a diving board is not present. The human body can move quite quickly underwater when diving as opposed to simply jumping in. There are minimum design constraints for diving pools (well depth, maximum allowable floor angles, head room, etc) for those very reasons - to protect a diver against head injury.
Best to always have a sign around a pool that states "NO DIVING" and make sure all guests and children are properly instructed. I've pulled my kids out of the pool and have made them sit out on 15min penalties when they disobey the rules. Embarrassed the heck out of my oldest son once when he did something stupid and I pulled him out while his friends got to stay in and play....he hasn't broken a pool rule since.