# Multi-marginal optimal transport and probabilistic graphical models

arXiv: https://arxiv.org/abs/2006.14113 · HTML: https://mlsanity.com/paper/2006.14113/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## Built on by (most cited first, 13 of 13)

- [Proximal Optimal Transport Modeling of Population Dynamics](https://mlsanity.com/paper/2106.06345/) (2021)
- [Neural Monge Map estimation and its applications](https://mlsanity.com/paper/2106.03812/) (2021)
- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [On the complexity of the optimal transport problem with graph-structured cost](https://mlsanity.com/paper/2110.00627/) (2021)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Contrasting Multiple Representations with the Multi-Marginal Matching Gap](https://mlsanity.com/paper/2405.19532/) (2024)
- [Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2212.14527/) (2022)
- [Data Assimilation for Sign-indefinite Priors: A generalization of Sinkhorn's algorithm](https://mlsanity.com/paper/2308.11791/) (2023)
- [Factored couplings in multi-marginal optimal transport via difference of convex programming](https://mlsanity.com/paper/2110.00629/) (2021)
- [Neural Estimation for Scaling Entropic Multimarginal Optimal Transport](https://mlsanity.com/paper/2506.00573/) (2025)
- [Optimal Multimarginal Schr"odinger Bridge: Minimum Spanning Tree over Measure-valued Vertices](https://mlsanity.com/paper/2509.10626/) (2025)
- [Information-Theoretic Equivalence of Entropic Multi-Marginal Optimal Transport: A Theory for Multi-Agent Communication](https://mlsanity.com/paper/2208.10256/) (2022)
- [Collision-based Dynamics for Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2412.16385/) (2024)

## Abstract (arXiv)

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular, an entropy regularized multi-marginal optimal transport is equivalent to a Bayesian marginal inference problem for probabilistic graphical models with the additional requirement that some of the marginal distributions are specified. This relation on the one hand extends the optimal transport as well as the probabilistic graphical model theories, and on the other hand leads to fast algorithms for multi-marginal optimal transport by leveraging the well-developed algorithms in Bayesian inference. Several numerical examples are provided to highlight the results.