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.
Introduces a sequential forward-backward diffusion framework that generates adapted time series by conditioning on prior history, with a parallelizable score-matching objective and statistical guarantees for ReLU networks.
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.
citing papers explorer
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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.
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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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Diffusion Models for Adaptive Sequential Data Generation
Introduces a sequential forward-backward diffusion framework that generates adapted time series by conditioning on prior history, with a parallelizable score-matching objective and statistical guarantees for ReLU networks.
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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.