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Communication Dans Un Congrès Année : 2022

Wavelet Score-Based Generative Modeling

Florentin Guth
  • Fonction : Auteur
  • PersonId : 1093562
Simon Coste
Valentin de Bortoli
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  • PersonId : 1084097
  • IdRef : 249460300

Résumé

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs typically requires a large number of time steps and hence a high computational cost. This is because of ill-conditioning properties of the score that we analyze mathematically. Previous approaches have relied on multiscale generation to considerably accelerate SGMs. We explain how this acceleration results from an implicit factorization of the data distribution into a product of conditional probabilities of wavelet coefficients across scales. The resulting Wavelet Score-based Generative Model (WSGM) synthesizes wavelet coefficients with the same number of time steps at all scales, and its time complexity therefore grows linearly with the image size. This is proved mathematically for Gaussian distributions, and shown numerically for physical processes at phase transition and natural image datasets.
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Dates et versions

hal-03959112 , version 1 (27-01-2023)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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  • HAL Id : hal-03959112 , version 1

Citer

Florentin Guth, Simon Coste, Valentin de Bortoli, Stéphane Mallat. Wavelet Score-Based Generative Modeling. 36th Conference on Neural Information Processing Systems (NeurIPS 2022)., Nov 2022, New Orleans (Louisiana), United States. ⟨hal-03959112⟩
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