For Gaussian mixture targets, diffusion discretization error and step complexity are controlled by latent entropy rather than ambient dimension.
Accelerating convergence of score-based diffusion models, provably
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The paper establishes an O(ε^{-4}) sample complexity bound for score estimation in diffusion models without requiring access to the empirical risk minimizer.
A Chebyshev-Gauss-Seidel higher-order sampler achieves d^{1+o(1)} ε^{-1/K} score complexity for TV distance ε under polynomial second-moment assumptions on the target.
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When Diffusion Model Can Ignore Dimension: An Entropy-Based Theory
For Gaussian mixture targets, diffusion discretization error and step complexity are controlled by latent entropy rather than ambient dimension.