Rethinking FID Through the Geometry of the Reference Dataset

Fréchet Inception Distance (FID) is widely used to evaluate image generators, yet lower FID does not always correspond to better sample quality. We show that this mismatch depends in part on the geometry of the reference dataset. In a controlled study across six datasets, distributional density and effective rank significantly explain how FID changes as sample quality improves. Concentrated datasets tend to yield more favorable FID trends, whereas more dispersed datasets can make FID worsen despite better samples. Attribution to precision and recall and ablations with alternative feature spaces and distances support the same conclusion. These results suggest that distributional metrics should be interpreted together with the geometry of the reference dataset for more reliable benchmarking.