Wavelet Score-Based Generative Modeling

• URL: http://arxiv.org/abs/2208.05003v1
• Date: Tue, 9 Aug 2022 19:13:34 GMT
• Title: Wavelet Score-Based Generative Modeling
• Authors: Florentin Guth, Simon Coste, Valentin De Bortoli, Stephane Mallat
• Abstract summary: We show that Wavelet Score-based Generative Model (WSGM) synthesizes wavelet coefficients with the same number of time steps at all scales. This is proved numerically over Gaussian distributions, and shown over physical processes at phase transition and natural image datasets.
• Score: 4.243926243206826
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. We show that SGMs can be considerably accelerated, by factorizing 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 over Gaussian distributions, and shown numerically over physical processes at phase transition and natural image datasets.

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