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Gaussian denoising has emerged as a powerful method for constructing simulation-free continuous normalizing flows for generative modeling.
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Logarithmic Sobolev inequalities
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From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
Sergey G. Bobkov and Michel Ledoux · 2000
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Monotonicity properties of optimal transportation and the FKG and related inequalities
Luis A. Caffarelli · 2000
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Keith Ball, Franck Barthe, and Assaf Naor · 2003
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Gradient of mutual information in linear vector Gaussian channels
Daniel P. Palomar and Sergio Verdú · 2005
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Gradient flows: In metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Lawrence C. Evans · 2010
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High-dimensional distributions with convexity properties
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Density estimation by dual ascent of the log-likelihood
Esteban G. Tabak and Eric Vanden-Eijnden · 2010
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Tweedie’s formula and selection bias
Bradley Efron · 2011
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Functional properties of minimum mean-square error and mutual information
Yihong Wu and Sergio Verdú · 2011
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A family of nonparametric density estimation algorithms
Esteban G. Tabak and Cristina V. Turner · 2013
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Analysis and geometry of Markov diffusion operators , volume 103
Dominique Bakry, Ivan Gentil, and Michel Ledoux · 2014
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Optimal detection of sparse mixtures against a given null distribution
Tony T. Cai and Yihong Wu · 2014
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Patrick Cattiaux and Arnaud Guillin · 2014
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NICE: Non-linear independent components estimation
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Generative adversarial nets
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Diederik P. Kingma and Max Welling · 2014
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Stochastic backpropagation and approximate inference in deep generative models
Danilo J. Rezende, Shakir Mohamed, and Daan Wierstra · 2014
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Log-concavity and strong log-concavity: A review
Adrien Saumard and Jon A. Wellner · 2014
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Variational inference with normalizing flows
Danilo J. Rezende and Shakir Mohamed · 2015
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Learning deep generative models
Ruslan Salakhutdinov · 2015
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Deep unsupervised learning using nonequilibrium thermodynamics
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli · 2015
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Deep Learning
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Lipschitz changes of variables between perturbations of log-concave measures
Maria Colombo, Alessio Figalli, and Yash Jhaveri · 2017
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Transport inequalities for log-concave measures, quantitative forms, and applications
Dario Cordero-Erausquin · 2017
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Information and estimation in Fokker-Planck channels
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Ricky T.Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K. Duvenaud · 2018
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Regularization under diffusion and anticoncentration of the information content
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An entropic generalization of Caffarelli’s contraction theorem via covariance inequalities
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Pierre Del Moral and Sumeetpal S. Singh · 2022
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Rectified flow: A marginal preserving approach to optimal transport
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Andre Wibisono and Varun Jog · 2018
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Monge-Ampère flow for generative modeling
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