Only the gradient component of score errors affects marginal distributions in diffusion models, so L2 error can be arbitrarily large with perfect match; this yields an impossibility result, a gradient-only KL bound, and a Sobolev estimator that correlates better with quality.
arXiv preprint arXiv:2409.07032 , year=
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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.
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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Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors
Only the gradient component of score errors affects marginal distributions in diffusion models, so L2 error can be arbitrarily large with perfect match; this yields an impossibility result, a gradient-only KL bound, and a Sobolev estimator that correlates better with quality.