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Diffusion Models are Minimax Optimal Distribution Estimators
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While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.
Forward citations
Cited by 2 Pith papers
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Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models
In overparameterized diffusion models, generalization happens first and memorization starts later, with the memorization time growing linearly with dataset size.
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Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models
With accurate score estimates, the probability flow ODE sampler reaches O(k/T) total-variation error, where k is the intrinsic dimension of the target distribution.
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