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This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
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Denoising diffusion probabilistic models
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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
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Analysis of high-dimensional distributions using pathwise methods
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Lee, H., Lu, J., and Tan, Y. (2022) · 2022
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Liu, X., Wu, L., Ye, M., and Liu, Q. (2022) · 2022
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Error bounds for flow matching methods
Benton, J., Deligiannidis, G., and Doucet, A. (2023) · 2023
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Fu, H., Yang, Z., Wang, M., and Chen, M. (2024) · 2024
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Convergence analysis for general probability flow odes of diffusion models in wasserstein distances
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Faster diffusion-based sampling with randomized midpoints: Sequential and parallel
Gupta, S., Cai, L., and Chen, S. (2024) · 2024
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Neural network-based score estimation in diffusion models: Optimization and generalization
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Provable acceleration for diffusion models under minimal assumptions
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Statistical efficiency of score matching: The view from isoperimetry
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Diffusion models are minimax optimal distribution estimators
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Diffusion models for time-series applications: a survey
Lin, L., Li, Z., Li, R., Li, X., and Gao, J. (2024) · 2024
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Linear convergence of diffusion models under the manifold hypothesis
Potaptchik, P., Azangulov, I., and Deligiannidis, G. (2024) · 2024
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Ren, Y., Chen, H., Rotskoff, G. M., and Ying, L. (2024) · 2024
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Diffusion models encode the intrinsic dimension of data manifolds
Stanczuk, J. P., Batzolis, G., Deveney, T., and Schönlieb, C.-B. (2024) · 2024
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Adaptivity of diffusion models to manifold structures
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A stochastic analysis approach to conditional diffusion guidance
Tang, W. and Xu, R. (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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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, C. H., Liang, F., and Liu, J. (2024) · 2024
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A precise asymptotic analysis of learning diffusion models: theory and insights
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On the generalization properties of diffusion models
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