# What Does Fr'echet Distance Measure? A Directional Decomposition

arXiv: https://arxiv.org/abs/2610.05518 · HTML: https://mlsanity.com/paper/2610.05518/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 53 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 30 of 40)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Quo Vadis, Action Recognition? A New Model and the Kinetics Dataset](https://mlsanity.com/paper/1705.07750/) (2017)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Towards Accurate Generative Models of Video: A New Metric & Challenges](https://mlsanity.com/paper/1812.01717/) (2018)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [ModelScope Text-to-Video Technical Report](https://mlsanity.com/paper/2308.06571/) (2023)
- [VideoMAE V2: Scaling Video Masked Autoencoders with Dual Masking](https://mlsanity.com/paper/2303.16727/) (2023)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Rethinking FID: Towards a Better Evaluation Metric for Image Generation](https://mlsanity.com/paper/2401.09603/) (2023)
- [Playground v2.5: Three Insights towards Enhancing Aesthetic Quality in Text-to-Image Generation](https://mlsanity.com/paper/2402.17245/) (2024)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Fr'echet Audio Distance: A Metric for Evaluating Music Enhancement Algorithms](https://mlsanity.com/paper/1812.08466/) (2018)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [Effectively Unbiased FID and Inception Score and where to find them](https://mlsanity.com/paper/1911.07023/) (2019)
- [Pros and Cons of GAN Evaluation Measures: New Developments](https://mlsanity.com/paper/2103.09396/) (2021)

## Abstract (arXiv)

The Fr'echet distance is a de facto standard for evaluating generative models across domains, appearing as FID for images and FVD for videos. It summarizes the discrepancy between generated and reference distributions in a single scalar, with lower values typically interpreted as better generation quality. However, this scalar view can obscure what drives the comparison. For example, in COCO dataset, increasing the number of diffusion sampling steps improves ImageReward scores yet worsens (increases) FID. Motivated by this mismatch, we seek to make the Fr'echet distance more interpretable by uncovering where the discrepancy lies. To this end, we introduce directional Fr'echet distance, the expected squared projection of the optimal transport displacement onto a given direction. Across our image, video, and protein case studies, we find that a small number of interpretable directions account for much of the distance. We use these directions to explain the FID increase in terms of semantic concepts represented by CLIP embeddings, quantify FVD's bias toward per-frame appearance, and revisit the interpretation of Protein FID. We open-source our codebase at https://github.com/yhlee-add/directional-fd.