# Fr'echet Wavelet Distance: A Domain-Agnostic Metric for Image Generation

arXiv: https://arxiv.org/abs/2312.15289 · HTML: https://mlsanity.com/paper/2312.15289/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 73 references that are in the map.
- First posted on arXiv 23 Dec 2023.

## Builds on (most cited first, 30 of 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Watch your Up-Convolution: CNN Based Generative Deep Neural Networks are Failing to Reproduce Spectral Distributions](https://mlsanity.com/paper/2003.01826/) (2020)
- [A Note on the Inception Score](https://mlsanity.com/paper/1801.01973/) (2018)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Projected GANs Converge Faster](https://mlsanity.com/paper/2111.01007/) (2021)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [Photorealistic Style Transfer via Wavelet Transforms](https://mlsanity.com/paper/1903.09760/) (2019)
- [Effectively Unbiased FID and Inception Score and where to find them](https://mlsanity.com/paper/1911.07023/) (2019)

## Built on by (most cited first, 9 of 9)

- [Population-Aligned Persona Generation for LLM-based Social Simulation](https://mlsanity.com/paper/2509.10127/) (2025)
- [Boosting Latent Diffusion with Perceptual Objectives](https://mlsanity.com/paper/2411.04873/) (2024)
- [AR-RAG: Autoregressive Retrieval Augmentation for Image Generation](https://mlsanity.com/paper/2506.06962/) (2025)
- [WaiT for the Signal: Simple Frequency-Aware Flow-Matching](https://mlsanity.com/paper/2607.28760/) (2026)
- [Solving Inverse Problems in Stochastic Self-Organizing Systems through Invariant Representations](https://mlsanity.com/paper/2506.11796/) (2025)
- [PRIVET: PRoximIty leakage detection Via Extreme value Theory](https://mlsanity.com/paper/2510.24233/) (2025)
- [Evaluating Text-to-Image and Text-to-Video Synthesis with a Conditional Fr'echet Distance](https://mlsanity.com/paper/2503.21721/) (2025)
- [APEX: Assumption-free Projection-based Embedding eXamination Metric for Generative Distribution Evaluation](https://mlsanity.com/paper/2605.07786/) (2026)
- [Decoding Register Tokens Preserves Global Scene Details](https://mlsanity.com/paper/2610.13299/) (2026)

## Abstract (arXiv)

Modern metrics for generative learning like Fr'echet Inception Distance (FID) and DINOv2-Fr'echet Distance (FD-DINOv2) demonstrate impressive performance. However, they suffer from various shortcomings, like a bias towards specific generators and datasets. To address this problem, we propose the Fr'echet Wavelet Distance (FWD) as a domain-agnostic metric based on the Wavelet Packet Transform (Wp). FWD provides a sight across a broad spectrum of frequencies in images with a high resolution, preserving both spatial and textural aspects. Specifically, we use Wp to project generated and real images to the packet coefficient space. We then compute the Fr'echet distance with the resultant coefficients to evaluate the quality of a generator. This metric is general-purpose and dataset-domain agnostic, as it does not rely on any pre-trained network, while being more interpretable due to its ability to compute Fr'echet distance per packet, enhancing transparency. We conclude with an extensive evaluation of a wide variety of generators across various datasets that the proposed FWD can generalize and improve robustness to domain shifts and various corruptions compared to other metrics.