Wavelet Score-Based Generative Modeling
This work addresses efficiency bottlenecks in generative modeling for applications like image synthesis, though it is incremental as it builds on existing SGM frameworks.
The paper tackles the high computational cost of score-based generative models (SGMs) by factorizing data distributions into wavelet coefficients across scales, resulting in the Wavelet Score-based Generative Model (WSGM) that accelerates synthesis with linear time complexity in image size, demonstrated on Gaussian distributions, physical processes, and natural images.
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.