The pressure of a fluid under gravity increases with depth. At a depth of 2 km below the surface, the pressure exerted by water on a body would be 200 times that of atmospheric pressure. This would collapse the lungs and other air pockets in the body and could damage other soft tissue.
What happens to the crushed remnants of the body depends on the net force acting on the body. If a human body is submerged under water, the parts that are at a greater depth are at a higher pressure than the parts that are higher. This pressure differential acting on the body exerts a net upward force on the body and this force is called the 'buoyant force'.
Gravity would try to pull you down and the buoyant force would try to push you up. What eventually happens depends on who wins the tug of war. And mathematically, if the density of the body is higher than the density of water, gravity wins and if not the buoyant force wins. So the density of the body would decide if the body would move up or down in water.
Normally the human body is less dense than water but if the lungs and other air pockets in the body collapse and crush, the body becomes more dense than water and hence would sink albeit slowly in water.