Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key idea of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, called RG-Flow, which can separate information at different scales of images with disentangled representations at each scale. We demonstrate our method mainly on the CelebA dataset and show that the disentangled representations at different scales enable semantic manipulation and style mixing of the images. To visualize the latent representations, we introduce receptive fields for flow-based models and find that the receptive fields learned by RG-Flow are similar to those in convolutional neural networks. In addition, we replace the widely adopted Gaussian prior distribution by a sparse prior distribution to further enhance the disentanglement of representations. From a theoretical perspective, the proposed method has $O(log L)$ complexity for image inpainting compared to previous generative models with $O(L^2)$ complexity.
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