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Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space.
Neural stochastic differential equations: Deep latent Gaussian models in the diffusion limit
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Integration by parts and time reversal for diffusion processes
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A view of the EM algorithm that justifies incremental, sparse, and other variants
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On Itô’s formula for multidimensional Brownian motion
Hans Föllmer and Philip Protter · 2000
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Diffusions, Markov processes and martingales: Volume 2, Itô calculus , volume 2
L Chris G Rogers and David Williams · 2000
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Radford M Neal · 2001
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Conditioned stochastic differential equations: theory, examples and application to finance
Fabrice Baudoin · 2002
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A sequential particle filter method for static models
Nicolas Chopin · 2002
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Reciprocal diffusions and symmetries of parabolic PDE: The nonflat case
Michèle Thieullen · 2002
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Slice sampling
Radford M Neal · 2003
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Stochastic differential equations
Bernt Øksendal · 2003
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Topics in optimal transportation
Cédric Villani · 2003
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Estimation of non-normalized statistical models by score matching
Aapo Hyvärinen and Peter Dayan · 2005
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Sequential Monte Carlo samplers
Pierre Del Moral, Arnaud Doucet, and Ajay Jasra · 2006
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Escorted free energy simulations: Improving convergence by reducing dissipation
Suriyanarayanan Vaikuntanathan and Christopher Jarzynski · 2008
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Optimal transport: old and new , volume 338
Cédric Villani et al · 2009
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Free energy computations: A mathematical perspective
Gabriel Stoltz, Mathias Rousset, et al · 2010
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A weak convergence approach to the theory of large deviations
Paul Dupuis and Richard S Ellis · 2011
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A dynamical systems framework for intermittent data assimilation
Sebastian Reich · 2011
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Bayesian inference with optimal maps
Tarek A El Moselhy and Youssef M Marzouk · 2012
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Convergence of probability measures
Patrick Billingsley · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Characterization of rare events in molecular dynamics
Carsten Hartmann, Ralf Banisch, Marco Sarich, Tomasz Badowski, and Christof Schütte · 2013
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Continuous martingales and Brownian motion , volume 293
Daniel Revuz and Marc Yor · 2013
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Reciprocal processes: a stochastic analysis approach
Sylvie Rœlly · 2013
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Transformation of measure on Wiener space
A Süleyman Üstünel and Moshe Zakai · 2013
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Annealed flow transport Monte Carlo
Michael Arbel, Alex Matthews, and Arnaud Doucet · 2021
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Yoshua Bengio, Salem Lahlou, Tristan Deleu, Edward J Hu, Mo Tiwari, and Emmanuel Bengio · 2021
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Stochastic control liaisons: Richard sinkhorn meets gaspard monge on a schrodinger bridge
Yongxin Chen, Tryphon T Georgiou, and Michele Pavon · 2021
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Diffusion Schrödinger bridge with applications to score-based generative modeling
Valentin De Bortoli, James Thornton, Jeremy Heng, and Arnaud Doucet · 2021
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Shooting Schrödinger’s cat
David Lopes Fernandes, Francisco Vargas, Carl Henrik Ek, and Neill DF Campbell · 2021
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An invitation to optimal transport, Wasserstein distances, and gradient flows
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Dominique Bakry, Ivan Gentil, Michel Ledoux, et al · 2014
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Auto-encoding variational Bayes
Diederik P Kingma and Max Welling · 2014
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Reciprocal processes. a measure-theoretical point of view
Christian Léonard, Sylvie Rœlly, and Jean-Claude Zambrini · 2014
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Stochastic backpropagation and approximate inference in deep generative models
Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra · 2014
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Applications of the cross-entropy method to importance sampling and optimal control of diffusions
Wei Zhang, Han Wang, Carsten Hartmann, Marcus Weber, and Christof Schütte · 2014
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Importance weighted autoencoders
Yuri Burda, Roger Grosse, and Ruslan Salakhutdinov · 2015
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Alessio Figalli and Federico Glaudo · 2021
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Mcmc variational inference via uncorrected hamiltonian annealing
Tomas Geffner and Justin Domke · 2021
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Gibbs flow for approximate transport with applications to Bayesian computation
Jeremy Heng, Arnaud Doucet, and Yvo Pokern · 2021
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Variational diffusion models
Diederik Kingma, Tim Salimans, Ben Poole, and Jonathan Ho · 2021
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Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Nikolas Nüsken and Lorenz Richter · 2021
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OT-flow: Fast and accurate continuous normalizing flows via optimal transport
Derek Onken, Samy Wu Fung, Xingjian Li, and Lars Ruthotto · 2021
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Normalizing flows for probabilistic modeling and inference
George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan · 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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Monte carlo variational auto-encoders
Achille Thin, Nikita Kotelevskii, Arnaud Doucet, Alain Durmus, Eric Moulines, and Maxim Panov · 2021
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Machine-learning approaches for the empirical Schrödinger bridge problem
Francisco Vargas · 2021
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Infinitely deep Bayesian neural networks with stochastic differential equations
Winnie Xu, Ricky T. Q. Chen, Xuechen Li, and David Duvenaud · 2021
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Differentiable annealed importance sampling and the perils of gradient noise
Guodong Zhang, Kyle Hsu, Jianing Li, Chelsea Finn, and Roger Grosse · 2021
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Differentiable annealed importance sampling and the perils of gradient noise
Guodong Zhang, Kyle Hsu, Jianing Li, Chelsea Finn, and Roger B Grosse · 2021
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Diffusion normalizing flow
Qinsheng Zhang and Yongxin Chen · 2021
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Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes
Wei Zhang · 2021
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An optimal control perspective on diffusion-based generative modeling
Julius Berner, Lorenz Richter, and Karen Ullrich · 2022
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Likelihood training of Schrödinger bridge using forward-backward SDEs theory
Tianrong Chen, Guan-Horng Liu, and Evangelos Theodorou · 2022
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Kamélia Daudel, Joe Benton, Yuyang Shi, and Arnaud Doucet · 2022
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Entropic neural optimal transport via diffusion processes
Nikita Gushchin, Alexander Kolesov, Alexander Korotin, Dmitry Vetrov, and Evgeny Burnaev · 2022
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Let us build bridges: Understanding and extending diffusion generative models
Xingchao Liu, Lemeng Wu, Mao Ye, et al · 2022
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Continual repeated annealed flow transport monte carlo
Alex Matthews, Michael Arbel, Danilo Jimenez Rezende, and Arnaud Doucet · 2022
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Flow annealed importance sampling bootstrap
Laurence Illing Midgley, Vincent Stimper, Gregor NC Simm, Bernhard Schölkopf, and José Miguel Hernández-Lobato · 2022
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Data assimilation: A dynamic homotopy-based coupling approach
Sebastian Reich · 2022
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First hitting diffusion models for generating manifold, graph and categorical data
Mao Ye, Lemeng Wu, and Qiang Liu · 2022
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Path integral sampler: A stochastic control approach for sampling
Qinsheng Zhang and Yongxin Chen · 2022
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Stochastic interpolants: A unifying framework for flows and diffusions
Michael S Albergo, Nicholas M Boffi, and Eric Vanden-Eijnden · 2023
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Langevin diffusion variational inference
Tomas Geffner and Justin Domke · 2023
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Adaptive annealed importance sampling with constant rate progress
Shirin Goshtasbpour, Victor Cohen, and Fernando Perez-Cruz · 2023
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Neural Lagrangian Schrödinger bridge: Diffusion modeling for population dynamics
Takeshi Koshizuka and Issei Sato · 2023
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Action matching: Learning stochastic dynamics from samples
Kirill Neklyudov, Rob Brekelmans, Daniel Severo, and Alireza Makhzani · 2023
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Interpolating between BSDEs and PINNs: Deep learning for elliptic and parabolic boundary value problems
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Diffusion bridge mixture transports, Schrödinger bridge problems and generative modeling
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Diffusion Schrödinger bridge matching
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A mean-field games laboratory for generative modeling
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Time-asymmetric protocol optimization for efficient free energy estimation
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Improved sampling via learned diffusions
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