# Sliced Wasserstein Generative Models

arXiv: https://arxiv.org/abs/1904.05408 · HTML: https://mlsanity.com/paper/1904.05408/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2019.

## Built on by (most cited first, 30 of 61)

- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [CFG-Zero*: Improved Classifier-Free Guidance for Flow Matching Models](https://mlsanity.com/paper/2503.18886/) (2025)
- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)
- [Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances](https://mlsanity.com/paper/2210.09160/) (2022)
- [Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections](https://mlsanity.com/paper/2106.15427/) (2021)
- [3D Pose Transfer with Correspondence Learning and Mesh Refinement](https://mlsanity.com/paper/2109.15025/) (2021)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Hierarchical Sliced Wasserstein Distance](https://mlsanity.com/paper/2209.13570/) (2022)
- [Wasserstein Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2110.07940/) (2021)
- [Unsupervised 3D Pose Transfer with Cross Consistency and Dual Reconstruction](https://mlsanity.com/paper/2211.10278/) (2022)
- [Self-Supervised Learning for Real-World Super-Resolution from Dual Zoomed Observations](https://mlsanity.com/paper/2203.01325/) (2022)
- [Amortized Projection Optimization for Sliced Wasserstein Generative Models](https://mlsanity.com/paper/2203.13417/) (2022)
- [Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flows](https://mlsanity.com/paper/2305.02164/) (2023)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Efficient Conditional GAN Transfer with Knowledge Propagation across Classes](https://mlsanity.com/paper/2102.06696/) (2021)
- [Generative Flows with Invertible Attentions](https://mlsanity.com/paper/2106.03959/) (2021)
- [Properties of Discrete Sliced Wasserstein Losses](https://mlsanity.com/paper/2307.10352/) (2023)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Representation Distribution Matching for One-Step Visual Generation](https://mlsanity.com/paper/2607.02375/) (2026)
- [Sharp bounds for max-sliced Wasserstein distances](https://mlsanity.com/paper/2403.00666/) (2024)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Lidar Upsampling with Sliced Wasserstein Distance](https://mlsanity.com/paper/2301.13558/) (2023)
- [Privacy-preserving data release leveraging optimal transport and particle gradient descent](https://mlsanity.com/paper/2401.17823/) (2024)
- [Image Generation with a Sphere Encoder](https://mlsanity.com/paper/2602.15030/) (2026)
- [Statistical and Topological Properties of Gaussian Smoothed Sliced Probability Divergences](https://mlsanity.com/paper/2110.10524/) (2021)
- [DigGAN: Discriminator gradIent Gap Regularization for GAN Training with Limited Data](https://mlsanity.com/paper/2211.14694/) (2022)
- [Tree-Sliced Wasserstein Distance: A Geometric Perspective](https://mlsanity.com/paper/2406.13725/) (2024)

## Abstract (arXiv)

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional distributions. In contrast, the sliced Wasserstein distance (SWD) factorizes high-dimensional distributions into their multiple one-dimensional marginal distributions and is thus easier to approximate. In this paper, we introduce novel approximations of the primal and dual SWD. Instead of using a large number of random projections, as it is done by conventional SWD approximation methods, we propose to approximate SWDs with a small number of parameterized orthogonal projections in an end-to-end deep learning fashion. As concrete applications of our SWD approximations, we design two types of differentiable SWD blocks to equip modern generative frameworks---Auto-Encoders (AE) and Generative Adversarial Networks (GAN). In the experiments, we not only show the superiority of the proposed generative models on standard image synthesis benchmarks, but also demonstrate the state-of-the-art performance on challenging high resolution image and video generation in an unsupervised manner.