Score-based generative models attain intrinsic Wasserstein-1 sample rates of order n to the power of -(beta+1)/(d+2beta) on d-dimensional smooth manifolds with beta-Holder densities.
arXiv preprint arXiv:2409.07032 , year=
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Diffusion models on manifold-supported data admit score decompositions whose statistical rates are controlled by intrinsic dimension and curvature.
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.
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Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds
Score-based generative models attain intrinsic Wasserstein-1 sample rates of order n to the power of -(beta+1)/(d+2beta) on d-dimensional smooth manifolds with beta-Holder densities.
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Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity
Diffusion models on manifold-supported data admit score decompositions whose statistical rates are controlled by intrinsic dimension and curvature.
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On the Robustness of Distribution Support under Diffusion Guidance
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.