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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For a broad class of coefficients, diffusion models achieve Õ(k/ε) iteration complexity for ε-accurate TV sampling under low-dimensional structure, independent of ambient dimension.
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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Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices
For a broad class of coefficients, diffusion models achieve Õ(k/ε) iteration complexity for ε-accurate TV sampling under low-dimensional structure, independent of ambient dimension.
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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.