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While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited.
The speed of mean glivenko-cantelli convergence
Dudley, R. M · 1969
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Monographs in mathematics vol. 99
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More on the estimation of distribution densities
Ibragimov, I. A. and Khas’minskii, R. Z · 1984
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Time Reversal of Diffusions
Haussmann, U. G. and Pardoux, E · 1986
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Barron, A. R · 1993
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Information-theoretic determination of minimax rates of convergence
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A global geometric framework for nonlinear dimensionality reduction
Tenenbaum, J. B., Silva, V. d., and Langford, J. C · 2000
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Estimation of non-normalized statistical models by score matching
Hyvärinen, A. and Dayan, P · 2005
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High-dimensional additive modeling
Meier, L., Van de Geer, S., and Bühlmann, P · 2009
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Tsybakov, A. B · 2009
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Rectified linear units improve restricted boltzmann machines
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Chernoff-type bounds for the gaussian error function
Chang, S.-H., Cosman, P. C., and Milstein, L. B · 2011
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Deep sparse rectifier neural networks
Glorot, X., Bordes, A., and Bengio, Y · 2011
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Entropy numbers in function spaces with mixed integrability
Triebel, H · 2011
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A connection between score matching and denoising autoencoders
Vincent, P · 2011
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Analysis and geometry of Markov diffusion operators , volume 103
Bakry, D., Gentil, I., Ledoux, M., et al · 2014
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U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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Deep unsupervised learning using nonequilibrium thermodynamics
Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and Ganguli, S · 2015
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Testing the manifold hypothesis
Fefferman, C., Mitter, S., and Narayanan, H · 2016
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Implicit regularization in matrix factorization
Gunasekar, S., Woodworth, B. E., Bhojanapalli, S., Neyshabur, B., and Srebro, N · 2017
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How well can generative adversarial networks learn densities: A nonparametric view
Liang, T · 2017
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Neural networks and rational functions
Telgarsky, M · 2017
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Error bounds for approximations with deep relu networks
Yarotsky, D · 2017
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Optimal approximation of piecewise smooth functions using deep relu neural networks
Petersen, P. and Voigtlaender, F · 2018
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Diffwave: A versatile diffusion model for audio synthesis
Kong, Z., Ping, W., Huang, J., Zhao, K., and Catanzaro, B · 2020
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Convergence and concentration of empirical measures under wasserstein distance in unbounded functional spaces
Lei, J · 2020
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Adaptive approximation and generalization of deep neural network with intrinsic dimensionality
Nakada, R. and Imaizumi, M · 2020
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Equivalence of approximation by convolutional neural networks and fully-connected networks
Petersen, P. and Voigtlaender, F · 2020
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Nonparametric regression using deep neural networks with relu activation function
Schmidt-Hieber, J · 2020
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Score-based generative modeling through stochastic differential equations
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Minimax distribution estimation in Wasserstein distance
Singh, S. and Póczos, B · 2018
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Nonparametric density estimation under adversarial losses
Singh, S., Uppal, A., Li, B., Li, C.-L., Zaheer, M., and Póczos, B · 2018
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The implicit bias of gradient descent on separable data
Soudry, D., Hoffer, E., Nacson, M. S., Gunasekar, S., and Srebro, N · 2018
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Adaptivity of deep relu network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality
Suzuki, T · 2018
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Implicit regularization in deep matrix factorization
Arora, S., Cohen, N., Hu, W., and Luo, Y · 2019
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Approximation and non-parametric estimation of resnet-type convolutional neural networks
Oono, K. and Suzuki, T · 2019
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Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B · 2020
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Universality of deep convolutional neural networks
Zhou, D.-X · 2020
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Diffusion schrödinger bridge with applications to score-based generative modeling
De Bortoli, V., Thornton, J., Heng, J., and Doucet, A · 2021
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Diffusion models beat gans on image synthesis
Dhariwal, P. and Nichol, A · 2021
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Statistical guarantees for generative models without domination
Schreuder, N., Brunel, V.-E., and Dalalyan, A · 2021
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Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic Besov space
Suzuki, T. and Nitanda, A · 2021
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Score-based generative modeling in latent space
Vahdat, A., Kreis, K., and Kautz, J · 2021
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Your diffusion model secretly knows the dimension of the data manifold
Batzolis, G., Stanczuk, J., and Schönlieb, C.-B · 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. R · 2022
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Convergence of denoising diffusion models under the manifold hypothesis
De Bortoli, V · 2022
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Ho, J., Salimans, T., Gritsenko, A., Chan, W., Norouzi, M., and Fleet, D. J · 2022
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Convergence of score-based generative modeling for general data distributions
Lee, H., Lu, J., and Tan, Y · 2022
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Minimax estimation of smooth densities in Wasserstein distance
Niles-Weed, J. and Berthet, Q · 2022
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Score-based generative models detect manifolds
Pidstrigach, J · 2022
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Hierarchical text-conditional image generation with clip latents
Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M · 2022
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