Bi-Lipschitz variance-preserving transport maps from Lipschitz scores are L1-dense among all probability densities, with KL convergence for Gaussian convolution targets.
Advancing Wasserstein convergence analysis of score-based models: Insights from discretization and second-order acceleration
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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.
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Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective
Bi-Lipschitz variance-preserving transport maps from Lipschitz scores are L1-dense among all probability densities, with KL convergence for Gaussian convolution targets.
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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.