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.
Florentin Guth is a PhD student at École Normale Supérieure in Paris, advised by Professor Stéphane Mallat. His research focuses on understanding the key properties of complex datasets on which deep architectures rely. This includes applications to image classification and generation tasks. He also works on modeling learned weights and representations and evaluating their robustness to architectural or dataset changes.
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