The area between these curves equals the Wasserstein Distance.
How It Works
Wasserstein Distance measures the minimum "work" needed to transform one distribution (Blue) into another (Red).
The Piles (Top Chart): Imagine the Blue bars are piles of dirt you have, and the Red bars are the shape you want to build.
The Work: You need to move the dirt. Moving 1 unit of dirt by 1 unit of distance costs 1 unit of work.
1D Trick: In one dimension, the Wasserstein Distance is exactly equal to the area between the Cumulative Distribution Functions (CDFs) (Bottom Chart).
Why it's better: Even if the piles don't overlap (Separate), there is a smooth distance value that tells you how far apart they are. Other metrics like KL Divergence might just say "Infinity" or "Max Difference" without indicating direction.