Kober, H. A theorem on Banach spaces. Compositio Mathematica, 7:135-140, 1940.
Koller, D. and Friedman, N. Probabilistic Graphical Models: Principles and Techniques. MIT press, 2009.
Korotin, A., Li, L., Solomon, J., and Burnaev, E. Continuous Wasserstein-2 barycenter estimation without minimax optimization. arXiv preprint arXiv:2102.01752, 2021.
Korotin, A., Egiazarian, V., Li, L., and Burnaev, E. Wasserstein iterative networks for barycenter estimation. arXiv preprint arXiv:2201.12245, 2022.
Kullback, S. Probability densities with given marginals. The Annals of Mathematical Statistics, 39 (4):1236-1243, 1968.
LeCun, Y. The MNIST database of handwritten digits. http://yann.lecun.com/exdb/mnist/, 1998.
Léonard, C. A survey of the Schrödinger problem and some of its connections with optimal transport. Discrete & Continuous Dynamical Systems-A, 34(4):1533-1574, 2014.
Li, L., Geneva, A., Yurochkin, M., and Solomon, J. M. Continuous regularized Wasserstein barycenters. Advances in Neural Information Processing Systems, 33:17755-17765, 2020.
Lipman, Y., Chen, R. T., Ben-Hamu, H., Nickel, M., and Le, M. Flow matching for generative modeling. International Conference on Learning Representations, 2023.
Luo, Z.-Q. and Tseng, P. On the convergence of the coordinate descent method for convex differentiable minimization. Journal of Optimization Theory and Applications, 72(1):7-35, 1992.
Makkuva, A., Taghvaei, A., Oh, S., and Lee, J. Optimal transport mapping via input convex neural networks. In International Conference on Machine Learning, pp. 6672-6681. PMLR, 2020.
Marino, S. D. and Gerolin, A. An optimal transport approach for the Schrödinger bridge problem and convergence of Sinkhorn algorithm. Journal of Scientific Computing, 85(2):27, 2020.
Mi, L., Yu, T., Bento, J., Zhang, W., Li, B., and Wang, Y. Variational Wasserstein barycenters for geometric clustering. arXiv preprint arXiv:2002.10543, 2020.
Minsker, S., Srivastava, S., Lin, L., and Dunson, D. Scalable and robust Bayesian inference via the median posterior. In International Conference on Machine Learning, pp. 1656-1664. PMLR, 2014.
Nichol, A. Q. and Dhariwal, P. Improved denoising diffusion probabilistic models. In International Conference on Machine Learning, pp. 8162-8171, 2021.
Nutz, M. Introduction to entropic optimal transport, 2021.
Pele, O. and Werman, M. Fast and robust Earth mover's distances. In 2009 IEEE 12th International Conference on Computer Vision, pp. 460-467. IEEE, 2009.
Peluchetti, S. Diffusion bridge mixture transports, Schrödinger bridge problems and generative modeling. arXiv preprint arXiv:2304.00917, 2023.
Peyre, G., Cuturi, M., et al. Computational optimal transport: With applications to data science. Foundations and Trends® in Machine Learning, 11(5-6):355-607, 2019.
Rabin, J., Peyre, G., Delon, J., and Bernot, M. Wasserstein barycenter and its application to texture mixing. In Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29-June 2, 2011, Revised Selected Papers 3, pp. 435-446. Springer, 2012.
Ruschendorf, L. Convergence of the Iterative Proportional Fitting procedure. The Annals of Statistics, pp. 1160-1174, 1995.
Schiebinger, G., Shu, J., Tabaka, M., Cleary, B., Subramanian, V., Solomon, A., Gould, J., Liu, S., Lin, S., Berube, P., et al. Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming. Cell, 176(4):928-943, 2019.