# Wasserstein Style Transfer

arXiv: https://arxiv.org/abs/1905.12828 · HTML: https://mlsanity.com/paper/1905.12828/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 21 of 21)

- [Exact Feature Distribution Matching for Arbitrary Style Transfer and Domain Generalization](https://mlsanity.com/paper/2203.07740/) (2022)
- [Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization](https://mlsanity.com/paper/2102.01752/) (2021)
- [Anomaly Detection under Distribution Shift](https://mlsanity.com/paper/2303.13845/) (2023)
- [Generating natural images with direct Patch Distributions Matching](https://mlsanity.com/paper/2203.11862/) (2022)
- [In the light of feature distributions: moment matching for Neural Style Transfer](https://mlsanity.com/paper/2103.07208/) (2021)
- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)
- [Gradual Domain Adaptation in the Wild:When Intermediate Distributions are Absent](https://mlsanity.com/paper/2106.06080/) (2021)
- [Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restoration](https://mlsanity.com/paper/2306.02342/) (2023)
- [Estimating Barycenters of Distributions with Neural Optimal Transport](https://mlsanity.com/paper/2402.03828/) (2024)
- [Energy-Guided Continuous Entropic Barycenter Estimation for General Costs](https://mlsanity.com/paper/2310.01105/) (2023)
- [Multi-Source and Test-Time Domain Adaptation on Multivariate Signals using Spatio-Temporal Monge Alignment](https://mlsanity.com/paper/2407.14303/) (2024)
- [Wasserstein Geodesic Generator for Conditional Distributions](https://mlsanity.com/paper/2308.10145/) (2023)
- [Learning representations that are closed-form Monge mapping optimal with application to domain adaptation](https://mlsanity.com/paper/2305.07500/) (2023)
- [Optimal Image Transport on Sparse Dictionaries](https://mlsanity.com/paper/2311.01984/) (2023)
- [Pairwise Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model](https://mlsanity.com/paper/2504.03188/) (2025)
- [Estimation of Stochastic Optimal Transport Maps](https://mlsanity.com/paper/2512.09499/) (2025)
- [Tunable Image Quality Control of 3-D Ultrasound using Switchable CycleGAN](https://mlsanity.com/paper/2112.02896/) (2021)
- [Connecting adversarial attacks and optimal transport for domain adaptation](https://mlsanity.com/paper/2205.15424/) (2022)
- [Non-Parametric Style Transfer](https://mlsanity.com/paper/2206.12921/) (2022)
- [Convolutional Monge Mapping Normalization for learning on sleep data](https://mlsanity.com/paper/2305.18831/) (2023)
- [GIST: Towards Photorealistic Style Transfer via Multiscale Geometric Representations](https://mlsanity.com/paper/2412.02214/) (2024)

## Abstract (arXiv)

We propose Gaussian optimal transport for Image style transfer in an Encoder/Decoder framework. Optimal transport for Gaussian measures has closed forms Monge mappings from source to target distributions. Moreover interpolates between a content and a style image can be seen as geodesics in the Wasserstein Geometry. Using this insight, we show how to mix different target styles , using Wasserstein barycenter of Gaussian measures. Since Gaussians are closed under Wasserstein barycenter, this allows us a simple style transfer and style mixing and interpolation. Moreover we show how mixing different styles can be achieved using other geodesic metrics between gaussians such as the Fisher Rao metric, while the transport of the content to the new interpolate style is still performed with Gaussian OT maps. Our simple methodology allows to generate new stylized content interpolating between many artistic styles. The metric used in the interpolation results in different stylizations.