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

TLDR; Water level goes down.  My guess is that the water level will go down when the ice has melted, because of the mass of the diamond will push the icecube further down into the water thereby raising the water level higher than it would be if it was an icecube only, resulting in a relatively lower water level when the water is displaced, since the ice doesn't displace that much because of the density when it turns into water.