# Reliable Modeling of Distribution Shifts via Displacement-Reshaped Optimal Transport

arXiv: https://arxiv.org/abs/2605.04965 · HTML: https://mlsanity.com/paper/2605.04965/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 21 of 21)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [Meta Optimal Transport](https://mlsanity.com/paper/2206.05262/) (2022)
- [Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds](https://mlsanity.com/paper/2403.06560/) (2024)
- [Inverse optimal transport](https://mlsanity.com/paper/1905.03950/) (2019)
- [Riemannian Metric Learning via Optimal Transport](https://mlsanity.com/paper/2205.09244/) (2022)
- [Making transport more robust and interpretable by moving data through a small number of anchor points](https://mlsanity.com/paper/2012.11589/) (2020)
- [Ground Metric Learning on Graphs](https://mlsanity.com/paper/1911.03117/) (2019)
- [Fast and Robust Comparison of Probability Measures in Heterogeneous Spaces](https://mlsanity.com/paper/2002.01615/) (2020)
- [Neural Optimal Transport with Lagrangian Costs](https://mlsanity.com/paper/2406.00288/) (2024)
- [Geodesic Sinkhorn for Fast and Accurate Optimal Transport on Manifolds](https://mlsanity.com/paper/2211.00805/) (2022)
- [Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem](https://mlsanity.com/paper/1709.10219/) (2017)
- [Learning transport cost from subset correspondence](https://mlsanity.com/paper/1909.13203/) (2019)
- [Learning Domain Invariant Representations by Joint Wasserstein Distance Minimization](https://mlsanity.com/paper/2106.04923/) (2021)
- [Feedback Schr"odinger Bridge Matching](https://mlsanity.com/paper/2410.14055/) (2024)
- [A Riemannian Approach to Ground Metric Learning for Optimal Transport](https://mlsanity.com/paper/2409.10085/) (2024)
- [Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomena](https://mlsanity.com/paper/2505.06123/) (2025)

## Abstract (arXiv)

Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not violate the true geometry of change. We propose Displacement-Reshaped Optimal Transport (ReshapeOT), a method that reshapes the ground metric by integrating observed sample displacements as an additional source of knowledge. Technically, ReshapeOT replaces the Euclidean metric with a Mahalanobis distance estimated from displacement second moments. This effectively carves expressways through the input space, inviting transport solutions that better align with observed displacements. Our method is computationally lightweight, integrates seamlessly into any OT solver that operates on a cost matrix, and can be kernelized for further flexibility. Experiments on synthetic and real-world data show that ReshapeOT achieves substantial gains in transport reliability. We further demonstrate our method's usefulness in two practical use cases.