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In this paper, we study the denoising diffusion probabilistic model (DDPM) inwavelet space, instead of pixel space, for visual synthesis. Considering thewavelet transform represents the image in spatial and frequency domains, wecarefully design a novel architecture SFUNet to effectively capture thecorrelation for both domains. Specifically, in the standard denoising U-Net forpixel data, we supplement the 2D convolutions and spatial-only attention layerswith our spatial frequency-aware convolution and attention modules to jointlymodel the complementary information from spatial and frequency domains inwavelet data. Our new architecture can be used as a drop-in replacement to thepixel-based network and is compatible with the vanilla DDPM training process.By explicitly modeling the wavelet signals, we find our model is able togenerate images with higher quality on CIFAR-10, FFHQ, LSUN-Bedroom, andLSUN-Church datasets, than the pixel-based counterpart.

Spatial-Frequency U-Net for Denoising Diffusion Probabilistic Models