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Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance.
Problem complexity and method efficiency in optimization
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The weighted particle method for convection-diffusion equations. i. the case of an isotropic viscosity
Pierre Degond and S Mas-Gallic · 1989
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Pierre Degond and Francisco-José Mustieles · 1990
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The variational formulation of the fokker–planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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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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Estimation of non-normalized statistical models by score matching
Aapo Hyvärinen and Peter Dayan · 2005
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Information geometry and its applications: Convex function and dually flat manifold
Shun-ichi Amari · 2008
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Robust stochastic approximation approach to stochastic programming
Arkadi Nemirovski, Anatoli Juditsky, Guanghui Lan, and Alexander Shapiro · 2009
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On pairs of f f -divergences and their joint range
Peter Harremoës and Igor Vajda · 2011
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A connection between score matching and denoising autoencoders
Pascal Vincent · 2011
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Convergence to equilibrium in wasserstein distance for fokker–planck equations
François Bolley, Ivan Gentil, and Arnaud Guillin · 2012
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Auto-encoding variational Bayes
Diederik P Kingma and Max Welling · 2013
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Thomas C. Sideris · 2013
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NICE: Non-linear independent components estimation
Laurent Dinh, David Krueger, and Yoshua Bengio · 2014
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Generative adversarial nets
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron C. Courville, and Yoshua Bengio · 2014
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Information geometry and its applications
Shun-ichi Amari · 2016
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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f-gan: Training generative neural samplers using variational divergence minimization
Sebastian Nowozin, Botond Cseke, and Ryota Tomioka · 2016
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Strong data processing inequalities and Φ \Phi -sobolev inequalities for discrete channels
Maxim Raginsky · 2016
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Input convex neural networks
Brandon Amos, Lei Xu, and J Zico Kolter · 2017
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Density estimation using Real NVP
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio · 2017
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Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martín Arjovsky, Vincent Dumoulin, and Aaron C. Courville · 2017
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Image-to-image translation with conditional adversarial networks
Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A. Efros · 2017
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On the ability of neural nets to express distributions
Holden Lee, Rong Ge, Tengyu Ma, Andrej Risteski, and Sanjeev Arora · 2017
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Unpaired image-to-image translation using cycle-consistent adversarial networks
Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros · 2017
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Langevin monte carlo and JKO splitting
Espen Bernton · 2018
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Neural ordinary differential equations
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 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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Glow: Generative flow with invertible 1x1 convolutions
Durk P Kingma and Prafulla Dhariwal · 2018
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Invertible residual networks
Jens Behrmann, Will Grathwohl, Ricky TQ Chen, David Duvenaud, and Jörn-Henrik Jacobsen · 2019
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A framework of composite functional gradient methods for generative adversarial models
Rie Johnson and Tong Zhang · 2019
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Variational wasserstein gradient flow
Jiaojiao Fan, Qinsheng Zhang, Amirhossein Taghvaei, and Yongxin Chen · 2022
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An error analysis of generative adversarial networks for learning distributions
Jian Huang, Yuling Jiao, Zhen Li, Shiao Liu, Yang Wang, and Yunfei Yang · 2022
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Variational inference via Wasserstein gradient flows
Marc Lambert, Sinho Chewi, Francis Bach, Silvère Bonnabel, and Philippe Rigollet · 2022
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Convergence for score-based generative modeling with polynomial complexity
Holden Lee, Jianfeng Lu, and Yixin Tan · 2022
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Rectified flow: A marginal preserving approach to optimal transport
Qiang Liu · 2022
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Neural estimation of statistical divergences
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An introduction to Variational Autoencoders
Diederik P. Kingma and Max Welling · 2019
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Generative modeling by estimating gradients of the data distribution
Yang Song and Stefano Ermon · 2019
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Theoretical guarantees for sampling and inference in generative models with latent diffusions
Belinda Tzen and Maxim Raginsky · 2019
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How to train your neural ODE: the world of jacobian and kinetic regularization
Chris Finlay, Jörn-Henrik Jacobsen, Levon Nurbekyan, and Adam Oberman · 2020
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Denoising diffusion probabilistic models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2020
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Normalizing flows: An introduction and review of current methods
Ivan Kobyzev, Simon JD Prince, and Marcus A Brubaker · 2020
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Sreejith Sreekumar and Ziv Goldfeld · 2022
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Invertible neural networks for graph prediction
Chen Xu, Xiuyuan Cheng, and Yao Xie · 2022
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On the capacity of deep generative networks for approximating distributions
Yunfei Yang, Zhen Li, and Yang Wang · 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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Building normalizing flows with stochastic interpolants
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Improved analysis of score-based generative modeling: User-friendly bounds under minimal smoothness assumptions
Hongrui Chen, Holden Lee, and Jianfeng Lu · 2023
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Restoration-degradation beyond linear diffusions: A non-asymptotic analysis for ddim-type samplers
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Forward-backward gaussian variational inference via JKO in the Bures-Wasserstein space
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Convergence of score-based generative modeling for general data distributions
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Flow matching for generative modeling
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Taming hyperparameter tuning in continuous normalizing flows using the jko scheme
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Computing high-dimensional optimal transport by flow neural networks
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Normalizing flow neural networks by JKO scheme
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Error bounds for flow matching methods
J Benton, G Deligiannidis, and A Doucet · 2024
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Nearly $d$-linear convergence bounds for diffusion models via stochastic localization
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The probability flow ode is provably fast
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Towards non-asymptotic convergence for diffusion-based generative models
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Distribution learning via neural differential equations: a nonparametric statistical perspective
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Improved convergence of score-based diffusion models via prediction-correction
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