Can You Solve this Ice Diamond Riddle? ft. Vsauce’s Michael Stevens

Assuming homogenous densities of the diamond and the ice cube and depending on the rations between the ice volume and the water volume on the instant the ice cube with the diamond was placed in the water there are 2 possibilities:
Either the combined density of ice cube with diamond is bigger or equal to water density and it sinks or has neutral bouncy. 
- in this case as the ice melts its bigger volume will be replaced by a smaller volume of water and the water level will drop.
In the second case when the combined density is smaller, and ice cube with diamond stays above water level.
- as the ice with melt the overall volume of the water:
Will decrease as ice underwater ice will melt and increase because the the ice cube has to sink a little more to compensate and stay afloat.
Those effects should cancel each out. 
So the overall water level will stay constant until the density is neutral.
After that the water level will drop as the ice melts.