# Debiased Sinkhorn barycenters

arXiv: https://arxiv.org/abs/2006.02575 · HTML: https://mlsanity.com/paper/2006.02575/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 30 of 34)

- [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023)
- [Automatic Text Evaluation through the Lens of Wasserstein Barycenters](https://mlsanity.com/paper/2108.12463/) (2021)
- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [Curriculum Reinforcement Learning using Optimal Transport via Gradual Domain Adaptation](https://mlsanity.com/paper/2210.10195/) (2022)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfe](https://mlsanity.com/paper/2201.00730/) (2022)
- [Wasserstein K-means for clustering probability distributions](https://mlsanity.com/paper/2209.06975/) (2022)
- [Discovering Conservation Laws using Optimal Transport and Manifold Learning](https://mlsanity.com/paper/2208.14995/) (2022)
- [Energy-Guided Continuous Entropic Barycenter Estimation for General Costs](https://mlsanity.com/paper/2310.01105/) (2023)
- [Doubly Regularized Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2303.11844/) (2023)
- [GeoECG: Data Augmentation via Wasserstein Geodesic Perturbation for Robust Electrocardiogram Prediction](https://mlsanity.com/paper/2208.01220/) (2022)
- [Optimal transport weights for causal inference](https://mlsanity.com/paper/2109.01991/) (2021)
- [Variational Wasserstein Barycenters with c-Cyclical Monotonicity](https://mlsanity.com/paper/2110.11707/) (2021)
- [Efficient Graph Field Integrators Meet Point Clouds](https://mlsanity.com/paper/2302.00942/) (2023)
- [Learning to Generate Wasserstein Barycenters](https://mlsanity.com/paper/2102.12178/) (2021)
- [Multiview Regenerative Morphing with Dual Flows](https://mlsanity.com/paper/2208.01287/) (2022)
- [Topological Node2vec: Enhanced Graph Embedding via Persistent Homology](https://mlsanity.com/paper/2309.08241/) (2023)
- [On the Existence of Optimal Transport Gradient for Learning Generative Models](https://mlsanity.com/paper/2102.05542/) (2021)
- [Landmarks Augmentation with Manifold-Barycentric Oversampling](https://mlsanity.com/paper/2104.00925/) (2021)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesics](https://mlsanity.com/paper/2302.02092/) (2023)
- [Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments](https://mlsanity.com/paper/2203.05813/) (2022)
- [Can LLMs predict the convergence of Stochastic Gradient Descent?](https://mlsanity.com/paper/2408.01736/) (2024)
- [Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization](https://mlsanity.com/paper/2501.14635/) (2025)
- [Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysis](https://mlsanity.com/paper/2505.13660/) (2025)
- [Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space](https://mlsanity.com/paper/2507.01709/) (2025)
- [An Homogeneous Unbalanced Regularized Optimal Transport model with applications to Optimal Transport with Boundary](https://mlsanity.com/paper/2201.02082/) (2022)
- [ScoreFusion: Fusing Score-based Generative Models via Kullback-Leibler Barycenters](https://mlsanity.com/paper/2406.19619/) (2024)
- [Linearized Wasserstein Barycenters: Synthesis, Analysis, Representational Capacity, and Applications](https://mlsanity.com/paper/2410.23602/) (2024)
- [Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphs](https://mlsanity.com/paper/2603.26940/) (2026)

## Abstract (arXiv)

Entropy regularization in optimal transport (OT) has been the driver of many recent interests for Wasserstein metrics and barycenters in machine learning. It allows to keep the appealing geometrical properties of the unregularized Wasserstein distance while having a significantly lower complexity thanks to Sinkhorn's algorithm. However, entropy brings some inherent smoothing bias, resulting for example in blurred barycenters. This side effect has prompted an increasing temptation in the community to settle for a slower algorithm such as log-domain stabilized Sinkhorn which breaks the parallel structure that can be leveraged on GPUs, or even go back to unregularized OT. Here we show how this bias is tightly linked to the reference measure that defines the entropy regularizer and propose debiased Wasserstein barycenters that preserve the best of both worlds: fast Sinkhorn-like iterations without entropy smoothing. Theoretically, we prove that the entropic OT barycenter of univariate Gaussians is a Gaussian and quantify its variance bias. This result is obtained by extending the differentiability and convexity of entropic OT to sub-Gaussian measures with unbounded supports. Empirically, we illustrate the reduced blurring and the computational advantage on various applications.