What Does Fr\'echet Distance Measure? A Directional Decomposition
This work addresses the limitation of the traditional Fréchet distance, which evaluates generative models via a single scalar that obscures the specific causes of distributional discrepancies and disconnects the metric from perceptual quality. We introduce the Directional Fréchet Distance, which decomposes optimal transport displacements through projection and leverages multimodal embeddings such as CLIP to map abstract distances onto interpretable semantic directions, revealing that a few key dimensions dominate most deviations. This approach successfully resolves conflicts between FID and human preferences in diffusion models, quantifies frame-wise appearance discrepancies in video FVD, and reinterprets the physical meaning of protein FID. By enabling fine-grained attribution analysis of generative quality across domains, this method provides a principled diagnostic tool for generative modeling. The code is publicly available.