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Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling.
Partial differential equations
Mikhailov, V · 1976
Earlier work this paper cites.
Décomposition polaire et réarrangement monotone des champs de vecteurs
Brenier, Y · 1987
Earlier work this paper cites.
The geometry of optimal transportation
Gangbo, W. and McCann, R. J · 1996
Earlier work this paper cites.
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
Benamou, J.-D. and Brenier, Y · 2000
Earlier work this paper cites.
The geometry of dissipative evolution equations: the porous medium equation
Otto, F · 2001
Earlier work this paper cites.
Clustering with bregman divergences
Banerjee, A., Merugu, S., Dhillon, I. S., Ghosh, J., and Lafferty, J · 2005
Earlier work this paper cites.
Estimation of non-normalized statistical models by score matching
Hyvärinen, A. and Dayan, P · 2005
Earlier work this paper cites.
Duality theorem for the stochastic optimal control problem
Mikami, T. and Thieullen, M · 2006
Earlier work this paper cites.
The porous medium equation: mathematical theory
Vázquez, J. L · 2007
Earlier work this paper cites.
Gradient flows: in metric spaces and in the space of probability measures
Ambrosio, L., Gigli, N., and Savaré, G · 2008
Earlier work this paper cites.
Optimal transport: old and new , volume 338
Villani, C · 2009
Earlier work this paper cites.
Score-based generative modeling through stochastic differential equations
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B · 2011
Earlier work this paper cites.
A kernel two-sample test
Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., and Smola, A · 2012
Earlier work this paper cites.
Sinkhorn distances: Lightspeed computation of optimal transport
Cuturi, M · 2013
Earlier work this paper cites.
A survey of the Schrödinger problem and some of its connections with optimal transport
Léonard, C · 2014
Earlier work this paper cites.
Single-cell chromatin accessibility reveals principles of regulatory variation
Buenrostro, J. D., Wu, B., Litzenburger, U. M., Ruff, D., Gonzales, M. L., Snyder, M. P., Chang, H. Y., and Greenleaf, W. J · 2015
Earlier work this paper cites.
Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells
Klein, A. M., Mazutis, L., Akartuna, I., Tallapragada, N., Veres, A., Li, V., Peshkin, L., Weitz, D. A., and Kirschner, M. W · 2015
Earlier work this paper cites.
Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets
Macosko, E. Z., Basu, A., Satija, R., Nemesh, J., Shekhar, K., Goldman, M., Tirosh, I., Bialas, A. R., Kamitaki, N., Martersteck, E. M., et al · 2015
Earlier work this paper cites.
U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
Earlier work this paper cites.
On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint
Chen, Y., Georgiou, T. T., and Pavon, M · 2016
Earlier work this paper cites.
Learning population-level diffusions with generative rnns
Hashimoto, T., Gifford, D., and Jaakkola, T · 2016
Earlier work this paper cites.
A new optimal transport distance on the space of finite radon measures
Kondratyev, S., Monsaingeon, L., and Vorotnikov, D · 2016
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Optimal transport in competition with reaction: The Hellinger–Kantorovich distance and geodesic curves
Liero, M., Mielke, A., and Savaré, G · 2016
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Improved techniques for training gans
Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., and Chen, X · 2016
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S · 2017
Cited alongside, same era.
Neural ordinary differential equations
Chen, R. T., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K · 2018
Cited alongside, same era.
Introduction to quantum mechanics
Griffiths, D. J. and Schroeter, D. F · 2018
An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows
Figalli, A. and Glaudo, F · 2021
Later among the works it cites.
Towards a mathematical theory of trajectory inference
Lavenant, H., Zhang, S., Kim, Y.-H., and Schiebinger, G · 2021
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Ot-flow: Fast and accurate continuous normalizing flows via optimal transport
Onken, D., Fung, S. W., Li, X., and Ruthotto, L · 2021
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Should ebms model the energy or the score?
Salimans, T. and Ho, J · 2021
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Reconstructing developmental landscapes and trajectories from single-cell data
Schiebinger, G · 2021
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Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures
Liero, M., Mielke, A., and Savaré, G · 2018
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Visualizing structure and transitions in high-dimensional biological data
Moon, K. R., van Dijk, D., Wang, Z., Gigante, S., Burkhardt, D. B., Chen, W. S., Yim, K., Elzen, A. v. d., Hirn, M. J., Coifman, R. R., et al · 2019
Cited alongside, same era.
Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming
Schiebinger, G., Shu, J., Tabaka, M., Cleary, B., Subramanian, V., Solomon, A., Gould, J., Liu, S., Lin, S., Berube, P., et al · 2019
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Generative modeling by estimating gradients of the data distribution
Song, Y. and Ermon, S · 2019
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How to train your neural ode: the world of jacobian and kinetic regularization
Finlay, C., Jacobsen, J.-H., Nurbekyan, L., and Oberman, A · 2020
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Denoising diffusion probabilistic models
Ho, J., Jain, A., and Abbeel, P · 2020
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Albergo, M. S. and Vanden-Eijnden, E · 2022
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Proximal optimal transport modeling of population dynamics
Bunne, C., Papaxanthos, L., Krause, A., and Cuturi, M · 2022
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Trajectory inference via mean-field langevin in path space
Chizat, L., Zhang, S., Heitz, M., and Schiebinger, G · 2022
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Optimal transport tools (ott): A jax toolbox for all things Wasserstein
Cuturi, M., Meng-Papaxanthos, L., Tian, Y., Bunne, C., Davis, G., and Teboul, O · 2022
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Manifold interpolating optimal-transport flows for trajectory inference
Huguet, G., Magruder, D. S., Fasina, O., Tong, A., Kuchroo, M., Wolf, G., and Krishnaswamy, S · 2022
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Flow matching for generative modeling
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Rectified flow: A marginal preserving approach to optimal transport
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Learning diffusion bridges on constrained domains
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Multisample flow matching: Straightening flows with minibatch couplings
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Diffusion schr \ \backslash " odinger bridge matching
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Conditional flow matching: Simulation-free dynamic optimal transport
Tong, A., Malkin, N., Huguet, G., Zhang, Y., Rector-Brooks, J., Fatras, K., Wolf, G., and Bengio, Y · 2023
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