# Conditional Frechet Inception Distance

arXiv: https://arxiv.org/abs/2103.11521 · HTML: https://mlsanity.com/paper/2103.11521/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 45 references that are in the map.
- First posted on arXiv 21 Mar 2021.

## Builds on (most cited first, 30 of 32)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Towards Accurate Generative Models of Video: A New Metric & Challenges](https://mlsanity.com/paper/1812.01717/) (2018)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Unsupervised Image-to-Image Translation Networks](https://mlsanity.com/paper/1703.00848/) (2017)
- [Toward Multimodal Image-to-Image Translation](https://mlsanity.com/paper/1711.11586/) (2017)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [cGANs with Projection Discriminator](https://mlsanity.com/paper/1802.05637/) (2018)
- [StackGAN++: Realistic Image Synthesis with Stacked Generative Adversarial Networks](https://mlsanity.com/paper/1710.10916/) (2017)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Effectively Unbiased FID and Inception Score and where to find them](https://mlsanity.com/paper/1911.07023/) (2019)
- [Classification Accuracy Score for Conditional Generative Models](https://mlsanity.com/paper/1905.10887/) (2019)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [Augmented CycleGAN: Learning Many-to-Many Mappings from Unpaired Data](https://mlsanity.com/paper/1802.10151/) (2018)
- [HYPE: A Benchmark for Human eYe Perceptual Evaluation of Generative Models](https://mlsanity.com/paper/1904.01121/) (2019)
- [Unsupervised Medical Image Translation Using Cycle-MedGAN](https://mlsanity.com/paper/1903.03374/) (2019)
- [Explorable Super Resolution](https://mlsanity.com/paper/1912.01839/) (2019)
- [An Improved Evaluation Framework for Generative Adversarial Networks](https://mlsanity.com/paper/1803.07474/) (2018)
- [On the Evaluation of Conditional GANs](https://mlsanity.com/paper/1907.08175/) (2019)
- [Evaluation Metrics for Conditional Image Generation](https://mlsanity.com/paper/2004.12361/) (2020)
- [Direct Speech-to-image Translation](https://mlsanity.com/paper/2004.03413/) (2020)
- [Subsampling Generative Adversarial Networks: Density Ratio Estimation in Feature Space with Softplus Loss](https://mlsanity.com/paper/1909.10670/) (2019)

## Built on by (most cited first, 16 of 16)

- [Learning Flow Fields in Attention for Controllable Person Image Generation](https://mlsanity.com/paper/2412.08486/) (2024)
- [Evaluating generative networks using Gaussian mixtures of image features](https://mlsanity.com/paper/2110.05240/) (2021)
- [A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging](https://mlsanity.com/paper/2306.01630/) (2023)
- [A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problems](https://mlsanity.com/paper/2210.13389/) (2022)
- [Semantics-Empowered Communication: A Tutorial-cum-Survey](https://mlsanity.com/paper/2212.08487/) (2022)
- [Learning few-step posterior samplers by unfolding and distillation of diffusion models](https://mlsanity.com/paper/2507.02686/) (2025)
- [A Unified Module for Accelerating STABLE-DIFFUSION: LCM-LORA](https://mlsanity.com/paper/2403.16024/) (2024)
- [SSD: Towards Better Text-Image Consistency Metric in Text-to-Image Generation](https://mlsanity.com/paper/2210.15235/) (2022)
- [DiffLoss: unleashing diffusion model as constraint for training image restoration network](https://mlsanity.com/paper/2406.19030/) (2024)
- [pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularization](https://mlsanity.com/paper/2411.00605/) (2024)
- [Diff-GOn: Enhancing Diffusion Models for Goal-Oriented Communications](https://mlsanity.com/paper/2412.06980/) (2024)
- [Cross-Modal Diffusion for Biomechanical Dynamical Systems Through Local Manifold Alignment](https://mlsanity.com/paper/2503.12214/) (2025)
- [Counterfactual Edits for Generative Evaluation](https://mlsanity.com/paper/2303.01555/) (2023)
- [Evaluating Text-to-Image and Text-to-Video Synthesis with a Conditional Fr'echet Distance](https://mlsanity.com/paper/2503.21721/) (2025)
- [A Proper Scoring Rule for Virtual Staining](https://mlsanity.com/paper/2602.23305/) (2026)
- [ReSAGE-PAR: Representational Similarity Assessment for Generative Expansion in Pedestrian Attribute Recognition](https://mlsanity.com/paper/2606.06020/) (2026)

## Abstract (arXiv)

We consider distance functions between conditional distributions. We focus on the Wasserstein metric and its Gaussian case known as the Frechet Inception Distance (FID). We develop conditional versions of these metrics, analyze their relations and provide a closed form solution to the conditional FID (CFID) metric. We numerically compare the metrics in the context of performance evaluation of modern conditional generative models. Our results show the advantages of CFID compared to the classical FID and mean squared error (MSE) measures. In contrast to FID, CFID is useful in identifying failures where realistic outputs which are not related to their inputs are generated. On the other hand, compared to MSE, CFID is useful in identifying failures where a single realistic output is generated even though there is a diverse set of equally probable outputs.