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Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI.
Reverse-time diffusion equation models
Anderson, B. D. (1982) · 1982
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Time reversal of diffusions
Haussmann, U. G. and Pardoux, E. (1986) · 1986
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Natural image statistics and neural representation
Simoncelli, E. P. and Olshausen, B. A. (2001) · 2001
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Estimation of non-normalized statistical models by score matching
Hyvärinen, A. (2005) · 2005
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Some extensions of score matching
Hyvärinen, A. (2007) · 2007
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Denoising diffusion implicit models
Song, J., Meng, C., and Ermon, S. (2020) · 2010
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A connection between score matching and denoising autoencoders
Vincent, P. (2011) · 2011
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High-dimensional probability: An introduction with applications in data science
Vershynin, R. (2018) · 2018
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Generative modeling by estimating gradients of the data distribution
Song, Y. and Ermon, S. (2019) · 2019
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High-dimensional statistics: A non-asymptotic viewpoint
Wainwright, M. J. (2019) · 2019
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Denoising diffusion probabilistic models
Ho, J., Jain, A., and Abbeel, P. (2020) · 2020
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DiffWave: A versatile diffusion model for audio synthesis
Kong, Z., Ping, W., Huang, J., Zhao, K., and Catanzaro, B. (2021) · 2021
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The intrinsic dimension of images and its impact on learning
Pope, P., Zhu, C., Abdelkader, A., Goldblum, M., and Goldstein, T. (2021) · 2021
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Score-based generative modeling through stochastic differential equations
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. (2021) · 2021
Cited alongside, same era.
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) · 2022
Cited alongside, same era.
Equivariant diffusion for molecule generation in 3d
Hoogeboom, E., Satorras, V. G., Vignac, C., and Welling, M. (2022) · 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) · 2022
Cited alongside, same era.
Diffusion models are minimax optimal distribution estimators
Oko, K., Akiyama, S., and Suzuki, T. (2023) · 2023
Later among the works it cites.
Convergence of diffusion models under the manifold hypothesis in high-dimensions
Azangulov, I., Deligiannidis, G., and Rousseau, J. (2024) · 2024
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Convergence analysis for general probability flow odes of diffusion models in wasserstein distances
Gao, X. and Zhu, L. (2024) · 2024
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Adapting to unknown low-dimensional structures in score-based diffusion models
Li, G. and Yan, Y. (2024) · 2024
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Linear convergence of diffusion models under the manifold hypothesis
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High-resolution image synthesis with latent diffusion models
Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. (2022) · 2022
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Photorealistic text-to-image diffusion models with deep language understanding
Saharia, C., Chan, W., Saxena, S., Li, L., Whang, J., Denton, E. L., Ghasemipour, K., Gontijo Lopes, R., Karagol Ayan, B., Salimans, T., et al. (2022) · 2022
Cited alongside, same era.
Phenaki: Variable length video generation from open domain textual descriptions
Villegas, R., Babaeizadeh, M., Kindermans, P.-J., Moraldo, H., Zhang, H., Saffar, M. T., Castro, S., Kunze, J., and Erhan, D. (2022) · 2022
Cited alongside, same era.
Diffusion models: A comprehensive survey of methods and applications
Yang, L., Zhang, Z., Song, Y., Hong, S., Xu, R., Zhao, Y., Shao, Y., Zhang, W., Cui, B., and Yang, M.-H. (2022) · 2022
Cited alongside, same era.
Diffusion models in vision: A survey
Croitoru, F.-A., Hondru, V., Ionescu, R. T., and Shah, M. (2023) · 2023
Cited alongside, same era.
Towards non-asymptotic convergence for diffusion-based generative models
Li, G., Wei, Y., Chen, Y., and Chi, Y. (2023) · 2023
Cited alongside, same era.
Linear convergence bounds for diffusion models via stochastic localization
Benton, J., De Bortoli, V., Doucet, A., and Deligiannidis, G. (2023a)
Cited in the paper.
Potaptchik, P., Azangulov, I., and Deligiannidis, G. (2024) · 2024
Later among the works it cites.
Tang, R., Lin, L., and Yang, Y. (2024) · 2024
Later among the works it cites.
Adaptivity of diffusion models to manifold structures
Tang, R. and Yang, 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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Diffusion models learn low-dimensional distributions via subspace clustering
Wang, P., Zhang, H., Zhang, Z., Chen, S., Ma, Y., and Qu, Q. (2024) · 2024
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O ( d / T ) O(d/T) convergence theory for diffusion probabilistic models under minimal assumptions
Li, G. and Yan, Y. (2025) · 2025
Closest in time.
Low-dimensional adaptation of diffusion models: Convergence in total variation
Liang, J., Huang, Z., and Chen, Y. (2025) · 2025
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