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In this paper, we investigate the latent geometry of generative diffusion models under the manifold hypothesis.
Reverse-time diffusion equation models
Anderson, B. D. (1982) · 1982
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Estimation of non-normalized statistical models by score matching
Hyvärinen, A. and Dayan, P. (2005) · 2005
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Manifold models for signals and images
Peyré, G. (2009) · 2009
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A connection between score matching and denoising autoencoders
Vincent, P. (2011) · 2011
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Testing the manifold hypothesis
Fefferman, C., Mitter, S., and Narayanan, H. (2016) · 2016
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Salimans, T., Karpathy, A., Chen, X., and Kingma, D. P. (2017) · 2017
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Modeling the influence of data structure on learning in neural networks: The hidden manifold model
Goldt, S., Mézard, M., Krzakala, F., and Zdeborová, L. (2020) · 2020
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Generalization in diffusion models arises from geometry-adaptive harmonic representations
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Diffusion models learn low-dimensional distributions via subspace clustering
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