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Regularity of the score function in generative models
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We study the regularity of the score function in score-based generative models and show that it naturally adapts to the smoothness of the data distribution. Under minimal assumptions, we establish Lipschitz estimates that directly support convergence and stability analyses in both diffusion and ODE-based generative models. In addition, we derive higher-order regularity bounds, which simplify existing arguments for optimally approximating the score function using neural networks.
Forward citations
Cited by 2 Pith papers
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Mimicking diffusion processes with differential equations
The probability-flow ODE yields a unique regular Lagrangian flow transporting p0 onto the diffusion marginals under Sobolev/BV score regularity, but Eulerian density uniqueness alone does not imply the existence of a ...
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Generalization bounds for score-based generative models: a synthetic proof
Score-based generative models achieve minimax optimal W1 rates n^{-(β+1)/(2β+d)} over β-Hölder densities, up to polylog factors.
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