← Back to slide 16Direction matters: coverage, not symmetric distance
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Direction Matters
Drag the orange source cluster. Coverage d(T→S) and off-target d(S→T) update live. Compare the two directed nearest-neighbor terms with Chamfer, Gaussian Fréchet distance and sliced Wasserstein. Swap source and target: the directed terms exchange values, while the symmetric distances stay fixed.
What changes when the roles swap?
Bars use one shared scale in squared feature units. Lower means closer by that definition; sizes across metrics are not performance rankings.
Source (train)
Target (benchmark)
Coverage distance d(T→S): mean over target points of the distance to the nearest source point
Off-target distance d(S→T): mean over source points of the distance to the nearest target point
This is a 2-D illustration using the paper’s squared nearest-neighbor definition and Chamfer sum. Each displayed point has equal mass within its dataset. Gaussian Fréchet uses the point clouds’ means and population covariances—the FID formula, without an Inception encoder. Sliced W₂² averages exact 1-D transport costs over 64 fixed projection directions; its square root is also shown. The paper reports sliced W₂, not full multidimensional W₂. These toy values are not research-result scores. Read the definitions and equations →