mlsanityData to 14 Oct 2026

A Wasserstein-type distance in the space of Gaussian Mixture Models

arXiv 1907.05254 ↗First posted 11 Jul 2019math.OCcited by 75

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Abstract (arXiv)

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We derive a very simple discrete formulation for this distance, which makes it suitable for high dimensional problems. We also study the corresponding multi-marginal and barycenter formulations. We show some properties of this Wasserstein-type distance, and we illustrate its practical use with some examples in image processing.

Key facts. Cited by 75 papers in the map (data through 14 Oct 2026). First posted on arXiv 11 Jul 2019.

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Citing papers per year: 2021: 5; 2022: 10; 2023: 11; 2024: 15; 2025: 23; 2026: 11.

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  1. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 101
  2. 2022Variational inference via Wasserstein gradient flowscited by 85
  3. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 46
  4. 2021Distributionally Robust Learningcited by 44
  5. 2023Analysis of learning a flow-based generative model from limited sample complexitycited by 38
  6. 2024Beyond FVD: Enhanced Evaluation Metrics for Video Generation Qualitycited by 22
  7. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  8. 2022Calibration tests beyond classificationcited by 20
  9. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  10. 2022Robust Bayesian Recoursecited by 18
  11. 2024Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errorscited by 16
  12. 2022Rethinking Initialization of the Sinkhorn Algorithmcited by 14
38 more
  1. 2025Mechanisms of Projective Composition of Diffusion Modelscited by 14
  2. 2025RegGS: Unposed Sparse Views Gaussian Splatting with 3DGS Registrationcited by 13
  3. 2022Small Transformers Compute Universal Metric Embeddingscited by 12
  4. 2021Evaluating generative networks using Gaussian mixtures of image featurescited by 11
  5. 2023A Bag-of-Prototypes Representation for Dataset-Level Applicationscited by 11
  6. 2024Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussianscited by 11
  7. 2025D2GS: Depth-and-Density Guided Gaussian Splatting for Stable and Accurate Sparse-View Reconstructioncited by 11
  8. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  9. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 9
  10. 2025Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGScited by 9
  11. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  12. 2023Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policiescited by 8
  13. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
  14. 2025Variational Inference with Mixtures of Isotropic Gaussianscited by 6
  15. 2026Concept Heterogeneity-aware Representation Steeringcited by 6
  16. 2024Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transportcited by 5
  17. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  18. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  19. 2023Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Spacecited by 4
  20. 2023Fast Dual Subgradient Optimization of the Integrated Transportation Distance Between Stochastic Kernelscited by 4
  21. 2024Optimal Transport on the Lie Group of Roto-translationscited by 4
  22. 2024Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixturescited by 4
  23. 2025Generative Distribution Embeddings: Lifting autoencoders to the space of distributions for multiscale representation learningcited by 4
  24. 2024Optimal Transport for Domain Adaptation through Gaussian Mixture Modelscited by 3
  25. 2024Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selectioncited by 3
  26. 2021Consistency issues in Gaussian Mixture Models reduction algorithmscited by 2
  27. 2022Unsupervised Opinion Summarisation in the Wasserstein Spacecited by 2
  28. 2022An Optimal Transport-driven Approach for Cultivating Latent Space in Online Incremental Learningcited by 2
  29. 2024What is the Right Notion of Distance between Predict-then-Optimize Tasks?cited by 2
  30. 2025Communication-Efficient and Personalized Federated Foundation Model Fine-Tuning via Tri-Matrix Adaptationcited by 2
  31. 2025On The Hidden Biases of Flow Matching Samplerscited by 2
  32. 2021Solving weakly supervised regression problem using low-rank manifold regularizationcited by 1
  33. 2023Domain Adaptation via Rebalanced Sub-domain Alignmentcited by 1
  34. 2023Robust probabilistic inference via a constrained transport metriccited by 1
  35. 2024Byzantine-tolerant distributed learning of finite mixture modelscited by 1
  36. 2024Optimal Transport for Probabilistic Circuitscited by 1
  37. 2025Federated Calculation of the Free-Support Transportation Barycenter by Single-Loop Dual Decompositioncited by 1
  38. 2025Measuring Time-Series Dataset Similarity using Wasserstein Distancecited by 1

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