# Wasserstein Distortion: Unifying Fidelity and Realism

arXiv: https://arxiv.org/abs/2310.03629 · HTML: https://mlsanity.com/paper/2310.03629/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 82 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 24 of 24)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Towards Faster and Stabilized GAN Training for High-fidelity Few-shot Image Synthesis](https://mlsanity.com/paper/2101.04775/) (2021)
- [Real-Time Adaptive Image Compression](https://mlsanity.com/paper/1705.05823/) (2017)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [Non-Stationary Texture Synthesis by Adversarial Expansion](https://mlsanity.com/paper/1805.04487/) (2018)
- [Deep Generative Models for Distribution-Preserving Lossy Compression](https://mlsanity.com/paper/1805.11057/) (2018)
- [NTIRE 2021 Challenge on Image Deblurring](https://mlsanity.com/paper/2104.14854/) (2021)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [A coding theorem for the rate-distortion-perception function](https://mlsanity.com/paper/2104.13662/) (2021)
- [Generating natural images with direct Patch Distributions Matching](https://mlsanity.com/paper/2203.11862/) (2022)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [Texture Interpolation for Probing Visual Perception](https://mlsanity.com/paper/2006.03698/) (2020)
- [Implicit Kernel Learning](https://mlsanity.com/paper/1902.10214/) (2019)
- [A Generative Model for Texture Synthesis based on Optimal Transport between Feature Distributions](https://mlsanity.com/paper/2007.03408/) (2020)
- [Texture Synthesis Through Convolutional Neural Networks and Spectrum Constraints](https://mlsanity.com/paper/1605.01141/) (2016)
- [High resolution neural texture synthesis with long range constraints](https://mlsanity.com/paper/2008.01808/) (2020)

## Built on by (most cited first, 8 of 8)

- [Good, Cheap, and Fast: Overfitted Image Compression with Wasserstein Distortion](https://mlsanity.com/paper/2412.00505/) (2024)
- [The Rate-Distortion-Perception Trade-off: The Role of Private Randomness](https://mlsanity.com/paper/2404.01111/) (2024)
- [Drop-In Perceptual Optimization for 3D Gaussian Splatting](https://mlsanity.com/paper/2603.23297/) (2026)
- [Advances in Diffusion-Based Generative Compression](https://mlsanity.com/paper/2601.18932/) (2026)
- [Seeing What Matters: Perceptual Wrapper with Common Randomness for 3D Gaussian Splatting](https://mlsanity.com/paper/2606.11782/) (2026)
- [Hand-4DGS: Feed-Forward 3D Gaussian Splatting for 4D Hand Reconstruction from Egocentric Videos](https://mlsanity.com/paper/2606.19156/) (2026)
- [JPEG AIC2026: A large-scale dataset for fine-grained assessment of image coding](https://mlsanity.com/paper/2607.22783/) (2026)
- [From Explicit References to Scene Manifolds: Distributional Fidelity and Realism for Radiance Field Quality Assessment](https://mlsanity.com/paper/2609.07346/) (2026)

## Abstract (arXiv)

We introduce a distortion measure for images, Wasserstein distortion, that simultaneously generalizes pixel-level fidelity on the one hand and realism or perceptual quality on the other. We show how Wasserstein distortion reduces to a pure fidelity constraint or a pure realism constraint under different parameter choices and discuss its metric properties. Pairs of images that are close under Wasserstein distortion illustrate its utility. In particular, we generate random textures that have high fidelity to a reference texture in one location of the image and smoothly transition to an independent realization of the texture as one moves away from this point. Wasserstein distortion attempts to generalize and unify prior work on texture generation, image realism and distortion, and models of the early human visual system, in the form of an optimizable metric in the mathematical sense.