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The recent, impressive advances in algorithmic generation of high-fidelity image, audio, and video are largely due to great successes in score-based diffusion models.
Reverse-time diffusion equation models
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Optimal uniform rate of convergence for nonparametric estimators of a density function or its derivatives
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Brownian Motion and Stochastic Calculus , volume 113 of Graduate Texts in Mathematics
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Generative Modeling with Denoising Auto-Encoders and Langevin Sampling
Block, A., Mroueh, Y., and Rakhlin, A. (2022) · 2002
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Estimation of non-normalized statistical models by score matching
Hyvärinen, A. (2005) · 2005
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Convergence rates of empirical bayes estimation in exponential family
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Optimal Transport: Old and New , volume 338
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Tweedie’s formula and selection bias
Efron, B. (2011) · 2011
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A connection between score matching and denoising autoencoders
Vincent, P. (2011) · 2011
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Minimax bounds for estimation of normal mixtures
Kim, A. K. H. (2014) · 2014
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Deep unsupervised learning using nonequilibrium thermodynamics
Sohl-Dickstein, J., Weiss, E. A., Maheswaranathan, N., and Ganguli, S. (2015) · 2015
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How well can generative adversarial networks learn densities: A nonparametric view
Liang, T. (2017) · 2017
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Probability for statisticians
Shorack, G. R. (2017) · 2017
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Generative Modeling by Estimating Gradients of the Data Distribution
Song, Y. and Ermon, S. (2019) · 2019
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WaveGrad: Estimating Gradients for Waveform Generation
Chen, N., Zhang, Y., Zen, H., Weiss, R. J., Norouzi, M., and Chan, W. (2020) · 2020
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Denoising Diffusion Probabilistic Models
Ho, J., Jain, A., and Abbeel, P. (2020) · 2020
Maximum likelihood training of score-based diffusion models
Song, Y., Durkan, C., Murray, I., and Ermon, S. (2021) · 2021
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Minimax bounds for estimating multivariate Gaussian location mixtures
Kim, A. K. H. and Guntuboyina, A. (2022) · 2022
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Convergence for score-based generative modeling with polynomial complexity
Lee, H., Lu, J., and Tan, Y. (2022) · 2022
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Minimax estimation of smooth densities in Wasserstein distance
Niles-Weed, J. and Berthet, Q. (2022) · 2022
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Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
Chen, S., Chewi, S., Li, J., Li, Y., Salim, A., and Zhang, A. (2023) · 2023
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Convergence of score-based generative modeling for general data distributions
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On relations between the relative entropy and χ 2 \chi^{2} -divergence, generalizations and applications
Nishiyama, T. and Sason, I. (2020) · 2020
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On the nonparametric maximum likelihood estimator for gaussian location mixture densities with application to gaussian denoising
Saha, S. and Guntuboyina, A. (2020) · 2020
Cited alongside, same era.
Improved Techniques for Training Score-Based Generative Models
Song, Y. and Ermon, S. (2020) · 2020
Cited alongside, same era.
Score-Based Generative Modeling through Stochastic Differential Equations
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. (2020) · 2020
Cited alongside, same era.
Diffusion Models Beat GANs on Image Synthesis
Dhariwal, P. and Nichol, A. (2021) · 2021
Cited alongside, same era.
Mathematical Foundations of Infinite-Dimensional Statistical Models
Giné, E. and Nickl, R. (2021) · 2021
Cited alongside, same era.
Lee, H., Lu, J., and Tan, Y. (2023) · 2023
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Diffusion models are minimax optimal distribution estimators
Oko, K., Akiyama, S., and Suzuki, T. (2023) · 2023
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Diffusion Models: A Comprehensive Survey of Methods and Applications
Yang, L., Zhang, Z., Song, Y., Hong, S., Xu, R., Zhao, Y., Zhang, W., Cui, B., and Yang, M.-H. (2023) · 2023
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An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization
Chen, M., Mei, S., Fan, J., and Wang, M. (2024) · 2024
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Information Theory: From Coding to Learning
Polyanskiy, Y. and Wu, Y. (2024) · 2024
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Score-based Diffusion Models via Stochastic Differential Equations – a Technical Tutorial
Tang, W. and Zhao, H. (2024) · 2024
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Optimal score estimation via empirical bayes smoothing
Wibisono, A., Wu, Y., and Yang, K. Y. (2024) · 2024
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Minimax optimality of score-based diffusion models: Beyond the density lower bound assumptions
Zhang, K., Yin, H., Liang, F., and Liu, J. (2024) · 2024
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