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We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples.
Ordinary differential equations, transport theory and sobolev spaces
Ronald J DiPerna and Pierre-Louis Lions · 1989
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Exponential convergence of Langevin distributions and their discrete approximations
Gareth O. Roberts and Richard L. Tweedie · 1996
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The variational formulation of the fokker–planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Generalization of an inequality by talagrand and links with the logarithmic sobolev inequality
F. Otto and C. Villani · 2000
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The Elements of Statistical Learning
Trevor Hastie, Robert Tibshirani, and Jerome Friedman · 2001
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The geometry of dissipative evolution equations: the porous medium equation
Felix Otto · 2001
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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 · 2005
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Pattern Recognition and Machine Learning (Information Science and Statistics)
Christopher M. Bishop · 2006
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A tutorial on energy-based learning
Yann LeCun, Sumit Chopra, Raia Hadsell, Marc’Aurelio Ranzato, and Fu-Jie Huang · 2006
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Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics Classics in Applied Mathemat)
Randall LeVeque · 2007
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L q L^{q} -functional inequalities and weighted porous media equations
Jean Dolbeault, Ivan Gentil, Arnaud Guillin, and Feng-Yu Wang · 2008
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Bayesian correlated clustering to integrate multiple datasets
Paul Kirk, Jim E Griffin, Richard S Savage, Zoubin Ghahramani, and David L Wild · 2012
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Auto-Encoding Variational Bayes
Diederik P Kingma and Max Welling · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Data integration for heterogenous datasets
James Hendler · 2014
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Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
Juan Luis Vázquez · 2014
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Deep unsupervised learning using nonequilibrium thermodynamics, 2015
Jascha Sohl-Dickstein, Eric A. Weiss, Niru Maheswaranathan, and Surya Ganguli · 2015
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Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
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Principal component analysis: A review and recent developments
Ian Jolliffe and Jorge Cadima · 2016
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Stein variational gradient descent: A general purpose bayesian inference algorithm
Qiang Liu and Dilin Wang · 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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Lecture notes on the diperna–lions theory in abstract measure spaces
Luigi Ambrosio and Dario Trevisan · 2017
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Numerical study of a particle method for gradient flows
José Antonio Carrillo, Yanghong Huang, Francesco Saverio Patacchini, and Gershon Wolansky · 2017
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Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
Alain Durmus and Eric Moulines · 2017
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Learning generative models with sinkhorn divergences, 2017
Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2017
Generative modeling by estimating gradients of the data distribution, 2020
Yang Song and Stefano Ermon · 2020
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A benchmark of batch-effect correction methods for single-cell rna sequencing data
Hoa Thi Nhu Tran, Kok Siong Ang, Marion Chevrier, Xiaomeng Zhang, Nicole Yee Shin Lee, Michelle Goh, and Jinmiao Chen · 2020
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Kale flow: A relaxed kl gradient flow for probabilities with disjoint support
Pierre Glaser, Michael Arbel, and Arthur Gretton · 2021
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Ot-flow: Fast and accurate continuous normalizing flows via optimal transport, 2021
Derek Onken, Samy Wu Fung, Xingjian Li, and Lars Ruthotto · 2021
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Fokker–planck particle systems for bayesian inference: Computational approaches
Sebastian Reich and Simon Weissmann · 2021
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Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 2017
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Stein variational gradient descent as gradient flow
Qiang Liu · 2017
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Least squares generative adversarial networks
X. Mao, Q. Li, H. Xie, R. K. Lau, Z. Wang, and S. Smolley · 2017
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Continuous-time flows for efficient inference and density estimation
Changyou Chen, Chunyuan Li, Liqun Chen, Wenlin Wang, Yunchen Pu, and Lawrence Carin Duke · 2018
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Neural ordinary differential equations
Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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Umap: Uniform manifold approximation and projection
Leland McInnes, John Healy, Nathaniel Saul, and Lukas Grossberger · 2018
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Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer · 2021
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Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Narain Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2021
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Score-based generative modeling in latent space
Arash Vahdat, Karsten Kreis, and Jan Kautz · 2021
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(f- γ \gamma )-divergences: Interpolating between f-divergences and integral probability metrics
Jeremiah Birrell, Paul Dupuis, Markos A Katsoulakis, Yannis Pantazis, and Luc Rey-Bellet · 2022
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Optimizing variational representations of divergences and accelerating their statistical estimation
Jeremiah Birrell, Markos A. Katsoulakis, and Yannis Pantazis · 2022
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Structure-preserving gans
Jeremiah Birrell, Markos A. Katsoulakis, Luc Rey-Bellet, and Wei Zhu · 2022
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Probability flow solution of the Fokker-Planck equation
Nicholas M. Boffi and Eric Vanden-Eijnden · 2022
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Formulation and properties of a divergence used to compare probability measures without absolute continuity
Paul Dupuis and Yixiang Mao · 2022
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Score-based generative models detect manifolds, 2022
Jakiw Pidstrigach · 2022
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Extracting training data from diffusion models
Nicolas Carlini, Jamie Hayes, Milad Nasr, Matthew Jagielski, Vikash Sehwag, Florian Tramer, Borja Balle, Daphne Ippolito, and Eric Wallace · 2023
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On memorization in diffusion models
Xiangming Gu, Chao Du, Tianyu Pang, Chongxuan Li, Min Lin, and Ye Wang · 2023
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Diffusion art or digital forgery? investigating data replication in diffusion models
Gowthami Somepalli, Vasu Singla, Micah Goldblum, Jonas Geiping, and Tom Goldstein · 2023
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Understanding and mitigating copying in diffusion models
Gowthami Somepalli, Vasu Singla, Micah Goldblum, Jonas Geiping, and Tom Goldstein · 2023
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A mean-field games laboratory for generative modeling, 2023
Benjamin J. Zhang and Markos A. Katsoulakis · 2023
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A good score does not lead to a good generative model
Sixu Li, Shi Chen, and Qin Li · 2024
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Wasserstein proximal operators describe score-based generative models and resolve memorization, 2024
Benjamin J. Zhang, Siting Liu, Wuchen Li, Markos A. Katsoulakis, and Stanley J. Osher · 2024
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