# Optimal transport for Gaussian mixture models

arXiv: https://arxiv.org/abs/1710.07876 · HTML: https://mlsanity.com/paper/1710.07876/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2017.

## Built on by (most cited first, 30 of 45)

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- [Rethinking Initialization of the Sinkhorn Algorithm](https://mlsanity.com/paper/2206.07630/) (2022)
- [Evaluating generative networks using Gaussian mixtures of image features](https://mlsanity.com/paper/2110.05240/) (2021)
- [Dynamical Wasserstein Barycenters for Time-series Modeling](https://mlsanity.com/paper/2110.06741/) (2021)
- [Hierarchical Refinement: Optimal Transport to Infinity and Beyond](https://mlsanity.com/paper/2503.03025/) (2025)
- [Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS](https://mlsanity.com/paper/2506.09534/) (2025)
- [Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates](https://mlsanity.com/paper/2301.11294/) (2023)
- [Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policies](https://mlsanity.com/paper/2305.10411/) (2023)
- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Variational Inference with Mixtures of Isotropic Gaussians](https://mlsanity.com/paper/2506.13613/) (2025)
- [Personalised Federated Learning On Heterogeneous Feature Spaces](https://mlsanity.com/paper/2301.11447/) (2023)
- [Wasserstein Gradient Flow over Variational Parameter Space for Variational Inference](https://mlsanity.com/paper/2310.16705/) (2023)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Space](https://mlsanity.com/paper/2310.11256/) (2023)
- [Mitigating Source Bias for Fairer Weak Supervision](https://mlsanity.com/paper/2303.17713/) (2023)
- [Perceptual Scales Predicted by Fisher Information Metrics](https://mlsanity.com/paper/2310.11759/) (2023)
- [Optimal Transport for Domain Adaptation through Gaussian Mixture Models](https://mlsanity.com/paper/2403.13847/) (2024)
- [Pixel Is Not a Barrier: An Effective Evasion Attack for Pixel-Domain Diffusion Models](https://mlsanity.com/paper/2408.11810/) (2024)
- [SwarmDiff: Swarm Robotic Trajectory Planning in Cluttered Environments via Diffusion Transformer](https://mlsanity.com/paper/2505.15679/) (2025)
- [Consistency issues in Gaussian Mixture Models reduction algorithms](https://mlsanity.com/paper/2104.12586/) (2021)
- [An Optimal Transport-driven Approach for Cultivating Latent Space in Online Incremental Learning](https://mlsanity.com/paper/2211.16780/) (2022)
- [Variational Online Mirror Descent for Robust Learning in Schr"odinger Bridge](https://mlsanity.com/paper/2504.02618/) (2025)
- [Shape-Preserving Dimensionality Reduction : An Algorithm and Measures of Topological Equivalence](https://mlsanity.com/paper/2106.02096/) (2021)
- [Expectation Distance-based Distributional Clustering for Noise-Robustness](https://mlsanity.com/paper/2110.08871/) (2021)
- [Fixed-point iterations for several dissimilarity measure barycenters in the Gaussian case](https://mlsanity.com/paper/2205.04806/) (2022)

## Abstract (arXiv)

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models. Basically, we study such models on a certain submanifold of probability densities with certain structure. Different aspects of this framework are discussed and several examples are presented to illustrate the results. This method represents our first attempt to study optimal transport problems for more general probability densities with structures.