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There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution.
Statistical analysis of non-lattice data
Julian Besag · 1975
Earlier work this paper cites.
Brownian motion and stochastic calculus , volume 113
Ioannis Karatzas and Steven E Shreve · 1991
Earlier work this paper cites.
Logarithmic sobolev inequalities for finite markov chains
Persi Diaconis and Laurent Saloff-Coste · 1996
Earlier work this paper cites.
Training products of experts by minimizing contrastive divergence
Geoffrey E Hinton · 2002
Earlier work this paper cites.
Markov chain decomposition for convergence rate analysis
Neal Madras and Dana Randall · 2002
Earlier work this paper cites.
Estimation of non-normalized statistical models by score matching
Aapo Hyvärinen · 2005
Earlier work this paper cites.
All of nonparametric statistics
Larry Wasserman · 2006
Earlier work this paper cites.
Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2011
Earlier work this paper cites.
A connection between score matching and denoising autoencoders
Pascal Vincent · 2011
Earlier work this paper cites.
A practical guide to training restricted boltzmann machines
Geoffrey E Hinton · 2012
Earlier work this paper cites.
Analysis and geometry of Markov diffusion operators , volume 103
Dominique Bakry, Ivan Gentil, Michel Ledoux, et al · 2014
Earlier work this paper cites.
Probability in high dimension
Ramon Van Handel · 2014
Earlier work this paper cites.
Linear estimating equations for exponential families with application to gaussian linear concentration models
Peter GM Forbes and Steffen Lauritzen · 2015
Earlier work this paper cites.
A theory of generative convnet
Jianwen Xie, Yang Lu, Song-Chun Zhu, and Yingnian Wu · 2016
Earlier work this paper cites.
Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S Dalalyan · 2017
Cited alongside, same era.
Markov chains and mixing times , volume 107
David A Levin and Yuval Peres · 2017
Cited alongside, same era.
Rényi differential privacy
Ilya Mironov · 2017
Cited alongside, same era.
High dimensional statistics
Phillippe Rigollet and Jan-Christian Hütter · 2017
Cited alongside, same era.
Density estimation in infinite dimensional exponential families
Bharath Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Aapo Hyvärinen, and Revant Kumar · 2017
Cited alongside, same era.
Reducibility and computational lower bounds for problems with planted sparse structure
Matthew Brennan, Guy Bresler, and Wasim Huleihel · 2018
Cited alongside, same era.
Poincaré and log–sobolev inequalities for mixtures
André Schlichting · 2019
Later among the works it cites.
Generative modeling by estimating gradients of the data distribution
Yang Song and Stefano Ermon · 2019
Later among the works it cites.
Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices
Santosh Vempala and Andre Wibisono · 2019
Later among the works it cites.
Learning deep kernels for exponential family densities
Li Wenliang, Danica J Sutherland, Heiko Strathmann, and Arthur Gretton · 2019
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Generative modeling with denoising auto-encoders and langevin sampling
Adam Block, Youssef Mroueh, and Alexander Rakhlin · 2020
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On the anatomy of mcmc-based maximum likelihood learning of energy-based models
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Learning generative convnets via multi-grid modeling and sampling
Ruiqi Gao, Yang Lu, Junpei Zhou, Song-Chun Zhu, and Ying Nian Wu · 2018
Cited alongside, same era.
Simulated tempering langevin monte carlo ii: An improved proof using soft markov chain decomposition
Rong Ge, Holden Lee, and Andrej Risteski · 2018
Cited alongside, same era.
Beyond log-concavity: Provable guarantees for sampling multi-modal distributions using simulated tempering langevin monte carlo
Holden Lee, Andrej Risteski, and Rong Ge · 2018
Cited alongside, same era.
Local optimality and generalization guarantees for the langevin algorithm via empirical metastability
Belinda Tzen, Tengyuan Liang, and Maxim Raginsky · 2018
Cited alongside, same era.
High-dimensional probability: An introduction with applications in data science , volume 47
Roman Vershynin · 2018
Cited alongside, same era.
Minimum stein discrepancy estimators
Alessandro Barp, Francois-Xavier Briol, Andrew Duncan, Mark Girolami, and Lester Mackey · 2019
Cited alongside, same era.
Erik Nijkamp, Mitch Hill, Tian Han, Song-Chun Zhu, and Ying Nian Wu · 2020
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Introduction to normalizing flows for lattice field theory
Michael S Albergo, Denis Boyda, Daniel C Hackett, Gurtej Kanwar, Kyle Cranmer, Sébastien Racaniere, Danilo Jimenez Rezende, and Phiala E Shanahan · 2021
Later among the works it cites.
Dimension-free log-sobolev inequalities for mixture distributions
Hong-Bin Chen, Sinho Chewi, and Jonathan Niles-Weed · 2021
Later among the works it cites.
Analysis of langevin monte carlo from poincaré to log-sobolev, 2021
Sinho Chewi, Murat A. Erdogdu, Mufan Bill Li, Ruoqi Shen, and Matthew Zhang · 2021
Later among the works it cites.
Normalizing flows and the real-time sign problem
Scott Lawrence and Yukari Yamauchi · 2021
Later among the works it cites.
Statistical efficiency of score matching: The view from isoperimetry
Frederic Koehler, Alexander Heckett, and Andrej Risteski · 2022
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High-resolution image synthesis with latent diffusion models
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer · 2022
Later among the works it cites.
Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions, 2023
Sitan Chen, Sinho Chewi, Jerry Li, Yuanzhi Li, Adil Salim, and Anru R. Zhang · 2023
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