The Wasserstein-1 distance (EMD) measures the minimum "work" to transform one distribution into another — the cost of moving earth from one pile to fill another.
Source distribution μ (click to add mass)
Target distribution ν (click to add mass)
Optimal transport plan
Uses 1D Wasserstein: sort both distributions and match quantiles. In 2D, solved via linear programming (north-west corner / Hungarian). The transport plan shows how mass flows from source (amber) to target (teal). Flow lines thickness = amount transported.