How can you infer that density decreases when ice melts from the water phase diagram? I know the phase diagram shows negative slope for water which is an exceptional case...  But how do you read that graph and get to the conclusion that density is increasing? 
It's the one with pressure plotted against temperature 
Thanks .. 

sorry i couldn't attach the graph here...
Draw an isotherm at a low enough temperature (&lt; the "triple point temperature of 0.01°C), so that it passes through "all three" phases (ignoring the high-pressure ices that are not relevant to the question).

Note that as pressure goes up you go from solid to liquid.  Increasing pressure always favors a denser phase, so liquid is denser than solid for water.

Water is not quite unique in this respect. Silicon and germanium are two elements that do the same thing.