# Differentiable Generalized Sliced Wasserstein Plans

arXiv: https://arxiv.org/abs/2505.22049 · HTML: https://mlsanity.com/paper/2505.22049/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 56 references that are in the map.
- First posted on arXiv 28 May 2025.

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

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [A framework for bilevel optimization that enables stochastic and global variance reduction algorithms](https://mlsanity.com/paper/2201.13409/) (2022)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Learning with minibatch Wasserstein : asymptotic and gradient properties](https://mlsanity.com/paper/1910.04091/) (2019)
- [Statistical and Topological Properties of Sliced Probability Divergences](https://mlsanity.com/paper/2003.05783/) (2020)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Conservative set valued fields, automatic differentiation, stochastic gradient method and deep learning](https://mlsanity.com/paper/1909.10300/) (2019)
- [Distributional Sliced-Wasserstein and Applications to Generative Modeling](https://mlsanity.com/paper/2002.07367/) (2020)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Amortized Implicit Differentiation for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2111.14580/) (2021)
- [Online Linear Optimization via Smoothing](https://mlsanity.com/paper/1405.6076/) (2014)
- [Globally Injective ReLU Networks](https://mlsanity.com/paper/2006.08464/) (2020)
- [Riemannian Residual Neural Networks](https://mlsanity.com/paper/2310.10013/) (2023)
- [Expected Sliced Transport Plans](https://mlsanity.com/paper/2410.12176/) (2024)
- [The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation](https://mlsanity.com/paper/2503.10636/) (2025)
- [Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections](https://mlsanity.com/paper/2211.10066/) (2022)
- [Augmented Sliced Wasserstein Distances](https://mlsanity.com/paper/2006.08812/) (2020)
- [DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Context](https://mlsanity.com/paper/2405.04923/) (2024)
- [Tree-Sliced Wasserstein Distance with Nonlinear Projection](https://mlsanity.com/paper/2505.00968/) (2025)

## Built on by (most cited first, 7 of 7)

- [Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances](https://mlsanity.com/paper/2509.20508/) (2025)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Efficient Transferable Optimal Transport via Min-Sliced Transport Plans](https://mlsanity.com/paper/2511.19741/) (2025)
- [Sliced-Regularized Optimal Transport](https://mlsanity.com/paper/2604.23944/) (2026)
- [ASAP: Amortized Doubly-Stochastic Attention via Sliced Dual Projection](https://mlsanity.com/paper/2605.12879/) (2026)
- [Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein](https://mlsanity.com/paper/2605.13753/) (2026)
- [Convergence of empirical subgradients for optimal transport-based objectives](https://mlsanity.com/paper/2605.28134/) (2026)

## Abstract (arXiv)

Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its formulation of OT plans. Its computational complexity remains a bottleneck, though, and slicing techniques have been developed to scale OT to large datasets. Recently, a novel slicing scheme, dubbed min-SWGG, lifts a single one-dimensional plan back to the original multidimensional space, finally selecting the slice that yields the lowest Wasserstein distance as an approximation of the full OT plan. Despite its computational and theoretical advantages, min-SWGG inherits typical limitations of slicing methods: (i) the number of required slices grows exponentially with the data dimension, and (ii) it is constrained to linear projections. Here, we reformulate min-SWGG as a bilevel optimization problem and propose a differentiable approximation scheme to efficiently identify the optimal slice, even in high-dimensional settings. We furthermore define its generalized extension for accommodating to data living on manifolds. Finally, we demonstrate the practical value of our approach in various applications, including gradient flows on manifolds and high-dimensional spaces, as well as a novel sliced OT-based conditional flow matching for image generation -- where fast computation of transport plans is essential.