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We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem.
A convexity principle for interacting gases
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On the geometry of the space of probability measures in Rn endowed with the quadratic optimal transport distance
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Optimal Transport: Old and New , volume 338
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A user’s guide to optimal transport
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MCMC methods for functions: Modifying old algorithms to make them faster
S. L. Cotter, G. O. Roberts, A. M. Stuart, and D. White · 2013
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The Bayesian approach to inverse problems
Masoumeh Dashti and Andrew M Stuart · 2013
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Martin Alnæs, Jan Blechta, Johan Hake, August Johansson, Benjamin Kehlet, Anders Logg, Chris Richardson, Johannes Ring, Marie E Rognes, and Garth N Wells · 2015
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Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
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Vector quantile regression: An optimal transport approach
Guillaume Carlier, Victor Chernozhukov, and Alfred Galichon · 2016
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Data-driven optimal transport
Giulio Trigila and Esteban G Tabak · 2016
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Input convex neural networks
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Variational inference: A review for statisticians
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Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows
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A generative flow for conditional sampling via optimal transport
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On the representation and learning of monotone triangular transport maps
Ricardo Baptista, Youssef Marzouk, and Olivier Zahm · 2023
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Y-Diagonal couplings: Approximating posteriors with conditional Wasserstein distances
Jannis Chemseddine, Paul Hagemann, and Christian Wald · 2023
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Efficient video prediction via sparsely conditioned flow matching
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Conditional sampling with monotone GANs: from generative models to likelihood-free inference
Ricardo Baptista, Bamdad Hosseini, Nikola B Kovachki, and Youssef Marzouk · 2020
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The frontier of simulation-based inference
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Fourier neural operator for parametric partial differential equations
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POT: Python optimal transport
Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, and Titouan Vayer · 2021
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Neural operator: Learning maps between function spaces
Nikola B. Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M. Stuart, and Anima Anandkumar · 2021
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Normalizing flows for probabilistic modeling and inference
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Timothy D Gebhard, Jonas Wildberger, Maximilian Dax, Daniel Angerhausen, Sascha P Quanz, and Bernhard Schölkopf · 2023
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Conditional optimal transport on function spaces
Bamdad Hosseini, Alexander W Hsu, and Amirhossein Taghvaei · 2023
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Diffusion generative models in infinite dimensions
Gavin Kerrigan, Justin Ley, and Padhraic Smyth · 2023
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Wasserstein geodesic generator for conditional distributions
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Score-based diffusion models in function space
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Multisample flow matching: Straightening flows with minibatch couplings
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Improving and generalizing flow-based generative models with minibatch optimal transport
Alexander Tong, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Rector-Brooks, Kilian Fatras, Guy Wolf, and Yoshua Bengio · 2023
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Zheyu Oliver Wang, Ricardo Baptista, Youssef Marzouk, Lars Ruthotto, and Deepanshu Verma · 2023
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Understanding the training of infinitely deep and wide ResNets with conditional optimal transport
Raphaël Barboni, Gabriel Peyré, and François-Xavier Vialard · 2024
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Conditional Wasserstein distances with applications in Bayesian OT flow matching
Jannis Chemseddine, Paul Hagemann, Christian Wald, and Gabriele Steidl · 2024
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Continuous-time functional diffusion processes
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Extended flow matching: a method of conditional generation with generalized continuity equation
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Functional flow matching
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Flow matching for scalable simulation-based inference
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