This releases introduces several new notable features. The less important but most exiting one being that we now have a logo for the toolbox (color and dark background) :

This logo is generated using with matplotlib and using the solution of an OT problem provided by POT (with ot.emd). Generating the logo can be done with a simple python script also provided in the documentation gallery.

New OT solvers include Weak OT and OT with factored coupling that can be used on large datasets. The Majorization Minimization solvers for non-regularized Unbalanced OT are now also available. We also now provide an implementation of GW and FGW unmixing and dictionary learning. It is now possible to use autodiff to solve entropic an quadratic regularized OT in the dual for full or stochastic optimization thanks to the new functions to compute the dual loss for entropic and quadratic regularized OT and reconstruct the OT plan on part or all of the data. They can be used for instance to solve OT problems with stochastic gradient or for estimating the dual potentials as neural networks.

On the backend front, we now have backend compatible functions and classes in the domain adaptation ot.da and unbalanced OT ot.unbalanced modules. This means that the DA classes can be used on tensors from all compatible backends. The free support Wasserstein barycenter solver is now also backend compatible.

Finally we have worked on the documentation to provide an update of existing examples in the gallery and and several new examples including GW dictionary learning weak Optimal Transport, NN based dual potentials estimation and Factored coupling OT. .

New features

  • Remove deprecated ot.gpu submodule (PR #361)

  • Update examples in the gallery (PR #359)

  • Add stochastic loss and OT plan computation for regularized OT and backend examples(PR #360)

  • Implementation of factored OT with emd and sinkhorn (PR #358)

  • A brand new logo for POT (PR #357)

  • Better list of related examples in quick start guide with minigallery (PR #334)

  • Add optional log-domain Sinkhorn implementation in WDA to support smaller values of the regularization parameter (PR #336)

  • Backend implementation for ot.lp.free_support_barycenter (PR #340)

  • Add weak OT solver + example (PR #341)

  • Add backend support for Domain Adaptation and Unbalanced solvers (PR #343)

  • Add (F)GW linear dictionary learning solvers + example (PR #319)

  • Add links to related PR and Issues in the doc release page (PR #350)

  • Add new minimization-maximization algorithms for solving exact Unbalanced OT + example (PR #362)

Closed issues

  • Fix mass gradient of ot.emd2 and ot.gromov_wasserstein2 so that they are centered (Issue #364, PR #363)

  • Fix bug in instantiating an autograd function ValFunction (Issue #337, PR #338)

  • Fix POT ABI compatibility with old and new numpy (Issue #346, PR #349)

  • Warning when feeding integer cost matrix to EMD solver resulting in an integer transport plan (Issue #345, PR #343)

  • Fix bug where gromov_wasserstein2 does not perform backpropagation with CUDA tensors (Issue #351, PR #352)

December 2021

This is a bug fix release that will remove the benchmarks module form the installation and correct the documentation generation.

Closed issues

  • Bug in documentation generation (tag VS master push, PR #332)

  • Remove installation of the benchmarks in global namespace (Issue #331, PR #333)


December 2021

This release fixes several bugs and introduces two new backends: Cupy and Tensorflow. Note that the tensorflow backend will work only when tensorflow has enabled the Numpy behavior (for transpose that is not by default in tensorflow). We also introduce a simple benchmark on CPU GPU for the sinkhorn solver that will be provided in the backend documentation.

This release also brings a few changes in dependencies and compatibility. First we removed tests for Python 3.6 that will not be updated in the future. Also note that POT now depends on Numpy (>= 1.20) because a recent change in ABI is making the wheels non-compatible with older numpy versions. If you really need an older numpy POT will work with no problems but you will need to build it from source.

As always we want to that the contributors who helped make POT better (and bug free).

New features

  • New benchmark for sinkhorn solver on CPU/GPU and between backends (PR #316)

  • New tensorflow backend (PR #316)

  • New Cupy backend (PR #315)

  • Documentation always up-to-date with README, RELEASES, CONTRIBUTING and CODE_OF_CONDUCT files (PR #316, PR #322).

Closed issues


November 2021

This new stable release introduces several important features.

First we now have an OpenMP compatible exact ot solver in ot.emd. The OpenMP version is used when the parameter numThreads is greater than one and can lead to nice speedups on multi-core machines.

Second we have introduced a backend mechanism that allows to use standard POT function seamlessly on Numpy, Pytorch and Jax arrays. Other backends are coming but right now POT can be used seamlessly for training neural networks in Pytorch. Notably we propose the first differentiable computation of the exact OT loss with ot.emd2 (can be differentiated w.r.t. both cost matrix and sample weights), but also for the classical Sinkhorn loss with ot.sinkhorn2, the Wasserstein distance in 1D with ot.wasserstein_1d, sliced Wasserstein with ot.sliced_wasserstein_distance and Gromov-Wasserstein with ot.gromov_wasserstein2. Examples of how this new feature can be used are now available in the documentation where the Pytorch backend is used to estimate a minimal Wasserstein estimator, a Generative Network (GAN), for a sliced Wasserstein gradient flow and optimizing the Gromov-Wassersein distance. Note that the Jax backend is still in early development and quite slow at the moment, we strongly recommend for Jax users to use the OTT toolbox when possible. As a result of this new feature, the old ot.gpu submodule is now deprecated since GPU implementations can be done using GPU arrays on the torch backends.

Other novel features include implementation for Sampled Gromov Wasserstein and Pointwise Gromov Wasserstein, Sinkhorn in log space with method='sinkhorn_log', Projection Robust Wasserstein, ans deviased Sinkorn barycenters.

This release will also simplify the installation process. We have now a pyproject.toml that defines the build dependency and POT should now build even when cython is not installed yet. Also we now provide pe-compiled wheels for linux aarch64 that is used on Raspberry PI and android phones and for MacOS on ARM processors.

Finally POT was accepted for publication in the Journal of Machine Learning Research (JMLR) open source software track and we ask the POT users to cite this paper from now on. The documentation has been improved in particular by adding a “Why OT?” section to the quick start guide and several new examples illustrating the new features. The documentation now has two version : the stable version corresponding to the last release and the master version that corresponds to the current master branch on GitHub.

As usual, we want to thank all the POT contributors (now 37 people have contributed to the toolbox). But for this release we thank in particular Nathan Cassereau and Kamel Guerda from the AI support team at IDRIS for their support to the development of the backend and OpenMP implementations.

New features

  • OpenMP support for exact OT solvers (PR #260)

  • Backend for running POT in numpy/torch + exact solver (PR #249)

  • Backend implementation of most functions in ot.bregman (PR #280)

  • Backend implementation of most functions in ot.optim (PR #282)

  • Backend implementation of most functions in ot.gromov (PR #294, PR #302)

  • Test for arrays of different type and device (CPU/GPU) (PR #304, #303)

  • Implementation of Sinkhorn in log space with method='sinkhorn_log' (PR #290)

  • Implementation of regularization path for L2 Unbalanced OT (PR #274)

  • Implementation of Projection Robust Wasserstein (PR #267)

  • Implementation of Debiased Sinkhorn Barycenters (PR #291)

  • Implementation of Sampled Gromov Wasserstein and Pointwise Gromov Wasserstein (PR #275)

  • Add pyproject.toml and build POT without installing cython first (PR #293)

  • Lazy implementation in log space for sinkhorn on samples (PR #259)

  • Documentation cleanup (PR #298)

  • Two up-to-date documentations for stable release and for master branch.

  • Building wheels on ARM for Raspberry PI and smartphones (PR #238)

  • Update build wheels to new version and new pythons (PR #236, #253)

  • Implementation of sliced Wasserstein distance (Issue #202, PR #203)

  • Add minimal build to CI and perform pep8 test separately (PR #210)

  • Speedup of tests and return run time (PR #262)

  • Add “Why OT” discussion to the documentation (PR #220)

  • New introductory example to discrete OT in the documentation (PR #191)

  • Add templates for Issues/PR on Github (PR#181)

Closed issues

  • Debug Memory leak in GAN example (#254)

  • DEbug GPU bug (Issue #284, #287, PR #288)

  • set_gradients method for JAX backend (PR #278)

  • Quicker GAN example for CircleCI build (PR #258)

  • Better formatting in Readme (PR #234)

  • Debug CI tests (PR #240, #241, #242)

  • Bug in Partial OT solver dummy points (PR #215)

  • Bug when Armijo linesearch (Issue #184, #198, #281, PR #189, #199, #286)

  • Bug Barycenter Sinkhorn (Issue 134, PR #195)

  • Infeasible solution in exact OT (Issues #126,#93, PR #217)

  • Doc for SUpport Barycenters (Issue #200, PR #201)

  • Fix labels transport in BaseTransport (Issue #207, PR #208)

  • Bug in emd_1d, non respected bounds (Issue #169, PR #170)

  • Removed Python 2.7 support and update codecov file (PR #178)

  • Add normalization for WDA and test it (PR #172, #296)

  • Cleanup code for new version of flake8 (PR #176)

  • Fixed requirements in (PR #174)

  • Removed specific MacOS flags (PR #175)


May 2020

This is the new stable release for POT. We made a lot of changes in the documentation and added several new features such as Partial OT, Unbalanced and Multi Sources OT Domain Adaptation and several bug fixes. One important change is that we have created the GitHub organization PythonOT that now owns the main POT repository and the repository for the new documentation is now hosted at

This is the first release where the Python 2.7 tests have been removed. Most of the toolbox should still work but we do not offer support for Python 2.7 and will close related Issues.

A lot of changes have been done to the documentation that is now hosted on instead of readthedocs. It was a hard choice but readthedocs did not allow us to run sphinx-gallery to update our beautiful examples and it was a huge amount of work to maintain. The documentation is now automatically compiled and updated on merge. We also removed the notebooks from the repository for space reason and also because they are all available in the example gallery. Note that now the output of the documentation build for each commit in the PR is available to check that the doc builds correctly before merging which was not possible with readthedocs.

The CI framework has also been changed with a move from Travis to Github Action which allows to get faster tests on Windows, MacOS and Linux. We also now report our coverage on and we have a reasonable 92% coverage. We also now generate wheels for a number of OS and Python versions at each merge in the master branch. They are available as outputs of this action. This will allow simpler multi-platform releases from now on.

In terms of new features we now have OTDA Classes for unbalanced OT, a new Domain adaptation class form multi domain problems (JCPOT), and several solvers to solve the Partial Optimal Transport problems.

This release is also the moment to thank all the POT contributors (old and new) for helping making POT such a nice toolbox. A lot of changes (also in the API) are coming for the next versions.


  • New documentation on (PR #160, PR #143, PR #144)

  • Documentation build on CircleCI with sphinx-gallery (PR #145,PR #146, #155)

  • Run sphinx gallery in CI (PR #146)

  • Remove notebooks from repo because available in doc (PR #156)

  • Build wheels in CI (#157)

  • Move from travis to GitHub Action for Windows, MacOS and Linux (PR #148, PR #150)

  • Partial Optimal Transport (PR#141 and PR #142)

  • Laplace regularized OTDA (PR #140)

  • Multi source DA with target shift (PR #137)

  • Screenkhorn algorithm (PR #121)

Closed issues

  • Add JMLR paper to the readme and Mathieu Blondel to the Acknoledgments (PR #231, #232)

  • Bug in Unbalanced OT example (Issue #127)

  • Clean Cython output when calling clean (Issue #122)

  • Various Macosx compilation problems (Issue #113, Issue #118, PR#130)

  • EMD dimension mismatch (Issue #114, Fixed in PR #116)

  • 2D barycenter bug for non square images (Issue #124, fixed in PR #132)

  • Bad value in EMD 1D (Issue #138, fixed in PR #139)

  • Log bugs for Gromov-Wassertein solver (Issue #107, fixed in PR #108)

  • Weight issues in barycenter function (PR #106)


July 2019

This is the first official stable release of POT and this means a jump to 0.6! The library has been used in the wild for a while now and we have reached a state where a lot of fundamental OT solvers are available and tested. It has been quite stable in the last months but kept the beta flag in its Pypi classifiers until now.

Note that this release will be the last one supporting officially Python 2.7 (See for more reasons). For next release we will keep the travis tests for Python 2 but will make them non necessary for merge in 2020.

The features are never complete in a toolbox designed for solving mathematical problems and research but with the new contributions we now implement algorithms and solvers from 24 scientific papers (listed in the file). New features include a direct implementation of the empirical Sinkhorn divergence, a new efficient (Cython implementation) solver for EMD in 1D and corresponding Wasserstein 1D. We now also have implementations for Unbalanced OT and a solver for Unbalanced OT barycenters. A new variant of Gromov-Wasserstein divergence called Fused Gromov-Wasserstein has been also contributed with exemples of use on structured data and computing barycenters of labeld graphs.

A lot of work has been done on the documentation with several new examples corresponding to the new features and a lot of corrections for the docstrings. But the most visible change is a new quick start guide for POT that gives several pointers about which function or classes allow to solve which specific OT problem. When possible a link is provided to relevant examples.

We will also provide with this release some pre-compiled Python wheels for Linux 64bit on github and pip. This will simplify the install process that before required a C compiler and numpy/cython already installed.

Finally we would like to acknowledge and thank the numerous contributors of POT that has helped in the past build the foundation and are still contributing to bring new features and solvers to the library.


  • Add compiled manylinux 64bits wheels to pip releases (PR #91)

  • Add quick start guide (PR #88)

  • Make doctest work on travis (PR #90)

  • Update documentation (PR #79, PR #84)

  • Solver for EMD in 1D (PR #89)

  • Solvers for regularized unbalanced OT (PR #87, PR#99)

  • Solver for Fused Gromov-Wasserstein (PR #86)

  • Add empirical Sinkhorn and empirical Sinkhorn divergences (PR #80)

Closed issues

  • Issue #59 fail when using “pip install POT” (new details in doc+ hopefully wheels)

  • Issue #85 Cannot run gpu modules

  • Issue #75 Greenkhorn do not return log (solved in PR #76)

  • Issue #82 Gromov-Wasserstein fails when the cost matrices are slightly different

  • Issue #72 Macosx build problem


Sep 2018

POT is 2 years old! This release brings numerous new features to the toolbox as listed below but also several bug correction.

Among the new features, we can highlight a non-regularized Gromov-Wasserstein solver, a new greedy variant of sinkhorn, non-regularized, convolutional (2D) and free support Wasserstein barycenters and smooth and stochastic implementation of entropic OT.

POT 0.5 also comes with a rewriting of ot.gpu using the cupy framework instead of the unmaintained cudamat. Note that while we tried to keed changes to the minimum, the OTDA classes were deprecated. If you are happy with the cudamat implementation, we recommend you stay with stable release 0.4 for now.

The code quality has also improved with 92% code coverage in tests that is now printed to the log in the Travis builds. The documentation has also been greatly improved with new modules and examples/notebooks.

This new release is so full of new stuff and corrections thanks to the old and new POT contributors (you can see the list in the readme).


  • Add non regularized Gromov-Wasserstein solver (PR #41)

  • Linear OT mapping between empirical distributions and 90% test coverage (PR #42)

  • Add log parameter in class EMDTransport and SinkhornLpL1Transport (PR #44)

  • Add Markdown format for Pipy (PR #45)

  • Test for Python 3.5 and 3.6 on Travis (PR #46)

  • Non regularized Wasserstein barycenter with scipy linear solver and/or cvxopt (PR #47)

  • Rename dataset functions to be more sklearn compliant (PR #49)

  • Smooth and sparse Optimal transport implementation with entropic and quadratic regularization (PR #50)

  • Stochastic OT in the dual and semi-dual (PR #52 and PR #62)

  • Free support barycenters (PR #56)

  • Speed-up Sinkhorn function (PR #57 and PR #58)

  • Add convolutional Wassersein barycenters for 2D images (PR #64)

  • Add Greedy Sinkhorn variant (Greenkhorn) (PR #66)

  • Big ot.gpu update with cupy implementation (instead of un-maintained cudamat) (PR #67)


Deprecated OTDA Classes were removed from ot.da and ot.gpu for version 0.5 (PR #48 and PR #67). The deprecation message has been for a year here since 0.4 and it is time to pull the plug.

Closed issues

  • Issue #35 : remove import plot from ot/ (See PR #41)

  • Issue #43 : Unusable parameter log for EMDTransport (See PR #44)

  • Issue #55 : UnicodeDecodeError: ‘ascii’ while installing with pip


15 Sep 2017

This release contains a lot of contribution from new contributors.


  • Automatic notebooks and doc update (PR #27)

  • Add gromov Wasserstein solver and Gromov Barycenters (PR #23)

  • emd and emd2 can now return dual variables and have max_iter (PR #29 and PR #25)

  • New domain adaptation classes compatible with scikit-learn (PR #22)

  • Proper tests with pytest on travis (PR #19)

  • PEP 8 tests (PR #13)

Closed issues

  • emd convergence problem du to fixed max iterations (#24)

  • Semi supervised DA error (#26)


11 Jul 2017

  • Correct bug in emd on windows


7 Jul 2017

  • emd* and sinkhorn* are now performed in parallel for multiple target distributions

  • emd and sinkhorn are for OT matrix computation

  • emd2 and sinkhorn2 are for OT loss computation

  • new notebooks for emd computation and Wasserstein Discriminant Analysis

  • relocate notebooks

  • update documentation

  • clean_zeros(a,b,M) for removimg zeros in sparse distributions

  • GPU implementations for sinkhorn and group lasso regularization


7 Apr 2017

  • New dimensionality reduction method (WDA)

  • Efficient method emd2 returns only tarnsport (in paralell if several histograms given)


5 Jan 2017

  • Add sphinx gallery for better documentation

  • Small efficiency tweak in sinkhorn

  • Add simple tic() toc() functions for timing


7 Nov 2016

  • numerical stabilization for sinkhorn (log domain and epsilon scaling)


4 Nov 2016

  • Update classes and examples for domain adaptation

  • Joint OT matrix and mapping estimation


31 Oct 2016

  • Original Domain adaptation classes


  • pipy works

First pre-release

28 Oct 2016

It provides the following solvers:

  • OT solver for the linear program/ Earth Movers Distance.

  • Entropic regularization OT solver with Sinkhorn Knopp Algorithm.

  • Bregman projections for Wasserstein barycenter [3] and unmixing.

  • Optimal transport for domain adaptation with group lasso regularization

  • Conditional gradient and Generalized conditional gradient for regularized OT.

Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.