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We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models.
Reverse-time diffusion equation models
Brian DO Anderson · 1982
Earlier work this paper cites.
The relaxation schemes for systems of conservation laws in arbitrary space dimensions
Shi Jin and Zhouping Xin · 1995
Earlier work this paper cites.
Partial Differential Equations
L.C. Evans · 1998
Earlier work this paper cites.
The variational formulation of the Fokker–Planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
Earlier work this paper cites.
Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science , volume 3
James Albert Sethian · 1999
Earlier work this paper cites.
Level set methods: an overview and some recent results
Stanley Osher and Ronald P Fedkiw · 2001
Earlier work this paper cites.
Convex optimization
Stephen Boyd, Stephen P Boyd, and Lieven Vandenberghe · 2004
Earlier work this paper cites.
An introduction to mathematical optimal control theory
Lawrence C Evans · 2005
Earlier work this paper cites.
Controlled Markov processes and viscosity solutions , volume 25
Wendell H Fleming and Halil Mete Soner · 2006
Earlier work this paper cites.
Large population stochastic dynamic games: closed-loop mckean-vlasov systems and the nash certainty equivalence principle
Minyi Huang, Roland P Malhamé, and Peter E Caines · 2006
Earlier work this paper cites.
Mean field games
Jean-Michel Lasry and Pierre-Louis Lions · 2007
Earlier work this paper cites.
Partial differential equations: An introduction
Walter A Strauss · 2007
Earlier work this paper cites.
Optimal transport: old and new , volume 338
Cédric Villani et al · 2009
Earlier work this paper cites.
Density estimation by dual ascent of the log-likelihood
Esteban G Tabak and Eric Vanden-Eijnden · 2010
Earlier work this paper cites.
Weighted energy-dissipation functionals for gradient flows
Alexander Mielke and Ulisse Stefanelli · 2011
Earlier work this paper cites.
A variational principle for gradient flows in metric spaces
Riccarda Rossi, Giuseppe Savaré, Antonio Segatti, and Ulisse Stefanelli · 2011
Earlier work this paper cites.
A connection between score matching and denoising autoencoders
Pascal Vincent · 2011
Earlier work this paper cites.
Mean field games equations with quadratic Hamiltonian: a specific approach
Olivier Guéant · 2012
Earlier work this paper cites.
Mean field games and mean field type control theory , volume 101
Alain Bensoussan, Jens Frehse, Phillip Yam, et al · 2013
Earlier work this paper cites.
Fluid mechanics
Bruce Roy Munson, Theodore Hisao Okiishi, Wade W Huebsch, and Alric P Rothmayer · 2013
Earlier work this paper cites.
A variational approach to gradient flows in metric spaces
Antonio Segatti · 2013
Earlier work this paper cites.
A family of nonparametric density estimation algorithms
Esteban G Tabak and Cristina V Turner · 2013
Earlier work this paper cites.
A survey of the Schrödinger problem and some of its connections with optimal transport
Christian Léonard · 2014
Earlier work this paper cites.
Variational inference with normalizing flows
Danilo Rezende and Shakir Mohamed · 2015
Earlier work this paper cites.
Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
Earlier work this paper cites.
Stein variational gradient descent: A general purpose Bayesian inference algorithm
Qiang Liu and Dilin Wang · 2016
Earlier work this paper cites.
GAN and VAE from an optimal transport point of view, 2017
Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2017
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{ \{ Euclidean, metric, and Wasserstein } \} gradient flows: an overview
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Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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