FHDMs achieve minimax optimal TV convergence rates for spherically supported Sobolev data distributions up to log factors, the first optimality result for random-time denoising diffusion models.
Jiachun Li, David Simchi-Levi, and Yunxiao Zhao
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The paper defines an intrinsic drift budget C_T in Fisher-Rao distance along the learner-environment trajectory and proves prequential reproducibility gaps bounded by order T^{-1/2} + C_T/T with a matching lower bound on regular subclasses.
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Statistical Convergence of Spherical First Hitting Diffusion Models
FHDMs achieve minimax optimal TV convergence rates for spherically supported Sobolev data distributions up to log factors, the first optimality result for random-time denoising diffusion models.
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Learning under Distributional Drift: Prequential Reproducibility as an Intrinsic Statistical Resource
The paper defines an intrinsic drift budget C_T in Fisher-Rao distance along the learner-environment trajectory and proves prequential reproducibility gaps bounded by order T^{-1/2} + C_T/T with a matching lower bound on regular subclasses.