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Wasserstein Gradient Flows (WGF) with respect to specific functionals have been widely used in the machine learning literature.
Implicit runge-kutta processes
John C Butcher · 1964
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The variational formulation of the fokker–planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Real analysis: modern techniques and their applications
Gerald B Folland · 1999
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An introduction to numerical analysis
Endre Süli and David F Mayers · 2003
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Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2005
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Induction over the Continuum
Iraj Kalantari · 2007
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Optimal transport: old and new
Cédric Villani et al · 2009
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Numerical solution of stochastic differential equations with jumps in finance
Eckhard Platen and Nicola Bruti-Liberati · 2010
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Playing atari with deep reinforcement learning
Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, and Martin Riedmiller · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
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Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
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Improved techniques for training gans
Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen · 2016
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Mastering the game of go with deep neural networks and tree search
David Silver, Aja Huang, Chris J Maddison, Arthur Guez, Laurent Sifre, George Van Den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al · 2016
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Input convex neural networks
Brandon Amos, Lei Xu, and J Zico Kolter · 2017
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
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Mmd gan: Towards deeper understanding of moment matching network
Chun-Liang Li, Wei-Cheng Chang, Yu Cheng, Yiming Yang, and Barnabás Póczos · 2017
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Computational optimal transport
Gabriel Peyré, Marco Cuturi, et al · 2017
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{ \{ Euclidean, metric, and Wasserstein
Filippo Santambrogio · 2017
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Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation
Bharath Bhushan Damodaran, Benjamin Kellenberger, Rémi Flamary, Devis Tuia, and Nicolas Courty · 2018
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Learning generative models with sinkhorn divergences
Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2018
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Ffjord: Free-form continuous dynamics for scalable reversible generative models
Will Grathwohl, Ricky TQ Chen, Jesse Bettencourt, Ilya Sutskever, and David Duvenaud · 2018
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Improving mmd-gan training with repulsive loss function
Wei Wang, Yuan Sun, and Saman Halgamuge · 2018
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Screening sinkhorn algorithm for regularized optimal transport
Mokhtar Z Alaya, Maxime Berar, Gilles Gasso, and Alain Rakotomamonjy · 2019
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Maximum mean discrepancy gradient flow
Michael Arbel, Anna Korba, Adil Salim, and Arthur Gretton · 2019
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Learning with minibatch wasserstein: asymptotic and gradient properties
Kilian Fatras, Younes Zine, Rémi Flamary, Rémi Gribonval, and Nicolas Courty · 2019
Cited alongside, same era.
Multi-source domain adaptation with sinkhorn barycenter
Tatsuya Komatsu, Tomoko Matsui, and Junbin Gao · 2021
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Do neural optimal transport solvers work? a continuous wasserstein-2 benchmark
Alexander Korotin, Lingxiao Li, Aude Genevay, Justin M Solomon, Alexander Filippov, and Evgeny Burnaev · 2021
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Large-scale wasserstein gradient flows
Petr Mokrov, Alexander Korotin, Lingxiao Li, Aude Genevay, Justin M Solomon, and Evgeny Burnaev · 2021
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Fast sinkhorn filters: Using matrix scaling for non-rigid shape correspondence with functional maps
Gautam Pai, Jing Ren, Simone Melzi, Peter Wonka, and Maks Ovsjanikov · 2021
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Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2021
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Interpolating between optimal transport and mmd using sinkhorn divergences
Jean Feydy, Thibault Séjourné, François-Xavier Vialard, Shun-ichi Amari, Alain Trouvé, and Gabriel Peyré · 2019
Cited alongside, same era.
Deep generative learning via variational gradient flow
Yuan Gao, Yuling Jiao, Yang Wang, Yao Wang, Can Yang, and Shunkang Zhang · 2019
Cited alongside, same era.
Sliced-wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
Antoine Liutkus, Umut Simsekli, Szymon Majewski, Alain Durmus, and Fabian-Robert Stöter · 2019
Cited alongside, same era.
Sinkhorn barycenters with free support via frank-wolfe algorithm
Giulia Luise, Saverio Salzo, Massimiliano Pontil, and Carlo Ciliberto · 2019
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Sobolev descent
Youssef Mroueh, Tom Sercu, and Anant Raj · 2019
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Generative modeling by estimating gradients of the data distribution
Yang Song and Stefano Ermon · 2019
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Sliced iterative normalizing flows
Biwei Dai and Uros Seljak · 2020
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Chao Zhang, Zhijian Li, Hui Qian, and Xin Du · 2021
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Wasserstein flow meets replicator dynamics: A mean-field analysis of representation learning in actor-critic
Yufeng Zhang, Siyu Chen, Zhuoran Yang, Michael Jordan, and Zhaoran Wang · 2021
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Optimizing functionals on the space of probabilities with input convex neural networks
David Alvarez-Melis, Yair Schiff, and Youssef Mroueh · 2022
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Proximal optimal transport modeling of population dynamics
Charlotte Bunne, Laetitia Papaxanthos, Andreas Krause, and Marco Cuturi · 2022
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Density ratio estimation via infinitesimal classification
Kristy Choi, Chenlin Meng, Yang Song, and Stefano Ermon · 2022
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Variational wasserstein gradient flow
Jiaojiao Fan, Qinsheng Zhang, Amirhossein Taghvaei, and Yongxin Chen · 2022
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Deep generative learning via euler particle transport
Yuan Gao, Jian Huang, Yuling Jiao, Jin Liu, Xiliang Lu, and Zhijian Yang · 2022
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Deep generative wasserstein gradient flows
Alvin Heng, Abdul Fatir Ansari, and Harold Soh · 2022
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Building normalizing flows with stochastic interpolants
Michael Samuel Albergo and Eric Vanden-Eijnden · 2023
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Image generation with shortest path diffusion
Ayan Das, Stathi Fotiadis, Anil Batra, Farhang Nabiei, FengTing Liao, Sattar Vakili, Da-shan Shiu, and Alberto Bernacchia · 2023
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Nonparametric generative modeling with conditional sliced-wasserstein flows
Chao Du, Tianbo Li, Tianyu Pang, YAN Shuicheng, and Min Lin · 2023
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Flow matching for generative modeling
Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matthew Le · 2023
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Flow straight and fast: Learning to generate and transfer data with rectified flow
Xingchao Liu, Chengyue Gong, and qiang liu · 2023
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Multisample flow matching: Straightening flows with minibatch couplings
Aram-Alexandre Pooladian, Heli Ben-Hamu, Carles Domingo-Enrich, Brandon Amos, Yaron Lipman, and Ricky Chen · 2023
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On kinetic optimal probability paths for generative models
Neta Shaul, Ricky TQ Chen, Maximilian Nickel, Matthew Le, and Yaron Lipman · 2023
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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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A mean-field games laboratory for generative modeling
Benjamin J Zhang and Markos A Katsoulakis · 2023
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