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

If the ice cube with diamond still floats  as normal ice cubes in normal water do, the it's easy: First, the ice-diamond-cube displaces as much water as it weighs, but after melting, the diamond sinks to the bottom and merely displaces according to its volume while the water from the molten ice displaces by, well, actually it diesn't matter - we may boldly assume that this water has the densiity water has (i.e., the differences in density between waters of different temperatures as occurring in the riddle situation are lower than between ice and water; also while the molten water ought to sink to the bottom when it reaches 4°C, we will not observe stable layers of different temperatures; instead, the waters will mix for an average temperature, which is essentially the reason we add ice cubes to drinks in the first place). So we may assume that the effect of the ice/water is zero, whereas the diamond displaces less in the end. The water level *sinks*

If on the oither hand the diamond makes the ice cube too heavy for floating to begin with, it will sink and melt there. But that means that diamond and ice displace accordng to their volume in the beginning and so do water and diamond in the end. Hence now the effect of the diamond is zero, whereas the ice/water displaces less in the end. The water level *sinks*

So far so good, but this raises a question:
* If the ice cube floats, the lower level is due to changing water displacement of the diamond alone
* If the ice cube sinks, the lower level is due to changing water displacement of the ice/water alone
How can there be such a discontinuity?
Well, I suppose that the answer is: There is none (or as the old Romans put it: natura non facit saltas ... nisi in theoria quantorum).
Actually, a floating diamond/ice cube will initially cause lower level because *some* ice melts and the remains will still float; during this phase, the change form the diamond displacing by weight to displacing by volume is only gradually. This continues until the diamond/ice cube has an average density matching the normal water and slowly submerges. As the melting continues, the density of the remaining cube rises above the water density and it will sink to the ground; after hitting that, all further melting happens according to the second paragraph above.