All boat dives have a DM in the water. Cayman Islands Watersport Association rule. The DM is usually out of the water early after guiding the divers back to where the boat is moored, leaving alone them to do explore the area under the boat. As long as you have air and ND time, you are ok'
Most ops will let you do your own thing once you have demonstrated proficiency for a dive or two and they get to know you. You will need to be back at the boat by the time specified in the briefing. Let them know you are going your own way before the dive to avoid confusion. Most ops will let you slip off the boat while the other divers are gearing up or heading down the line. If you are in the middle of a dive and want to go your own way, don't just disappear, let the DM know before swimming away.
If you do something stupid, you will be put back on a leash. I would include, running out of air, losing your buddy, going into deco, staying down long after specified dive time and getting lost; as stupid. The dive ops all prioritize safety and don't have much tolerance.
I sometimes like to hang with the DM/guide. They usually have good eyes and skills and you can learn a lot by diving with them. If the area has complex navigation, my buddy doesn't trust me anyway, so we end up hanging with the DM.
