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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Extends Tweedie's formulae to GBM, BESQ, and CIR processes to enable non-Gaussian diffusion generative models and empirical Bayes applications.
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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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Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian
Extends Tweedie's formulae to GBM, BESQ, and CIR processes to enable non-Gaussian diffusion generative models and empirical Bayes applications.