Do any mobs dive after you?

If a mob is chasing you, and the only way to get you is by diving under water, will they dive under water?

I know they swim to get you, but I've never seen them diving.

Solution 1:

No, hostile mobs can't navigate water very well, and they won't specifically dive for you.

Either they automatically float to the top at all times — most of them do — or they sink to the bottom. Iron Golems will for example will not even chase you into water because they can't swim at all and will sink like a rock.

Solution 2:

Most of the mobs' behavior in water is the equivalent of you constantly holding space bar. i.e. they are always trying to swim to the surface.

(although some dont, also n.b. iron golems don't swim and also don't drown)