Why diffusion denoising-based generative methods do not suffer the curse of dimensionality even though the data may lie on extremely high-dim spaces? Our new work, accepted by the JMLR: https://arxiv.org/abs/2409.02426 reveals the not-so-surprising secret: as long as the intrinsic dimension of the distribution is low, the generative process can be extremely efficient and effective!
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#423Why diffusion denoising-based generative methods do not suffer the curse of dimensionality even though the data may lie in extremely high-dim spaces? Our new work, accepted by the JMLR: https://arxiv.org/abs/2409.02426 reveals the not-so-surprising secret: as long as the intrinsic dimension of the distribution is very low, the generative process can be extremely efficient and effective! It seems that a mixture of low-rank Gaussians is a universal model for all informative real-world data. as we stipulated in a former textbook of mine: Generalized Principal Component Analysis: http://www.vision.jhu.edu/gpca/, published exactly ten years ago!
Why diffusion denoising-based generative methods do not suffer the curse of dimensionality even though the data may lie on extremely high-dim spaces? Our new work, accepted by the JMLR: https://arxiv.org/abs/2409.02426 reveals the not-so-surprising secret: as long as the intrinsic dimension of the distribution is low, the generative process can be extremely efficient and effective! It seems that a mixture of low-rank Gaussians is a universal model for all informative real-world data. as we stipulated in a former textbook of mine: Generalized Principal Component Analysis: http://www.vision.jhu.edu/gpca/, published exactly ten years ago!
Why diffusion denoising-based generative methods do not suffer the curse of dimensionality even though the data may lie on extremely high-dim spaces? Our new work, accepted by the JMLR: https://arxiv.org/abs/2409.02426 reveals the not-so-surprising secret: as long as the intrinsic dimension of the distribution is very low, the generative process can be extremely efficient and effective! It seems that a mixture of low-rank Gaussians is a universal model for all informative real-world data. as we stipulated in a former textbook of mine: Generalized Principal Component Analysis: http://www.vision.jhu.edu/gpca/, published exactly ten years ago!
@YiMaTweets sample complexity scaling with intrinsic dimension. people assumed this already right? good to see actual proof.
