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Abstract

Classical generative diffusion models learn an isotropic Gaussian denoising
process, treating all spatial regions uniformly, thus neglecting potentially
valuable structural information in the data. Inspired by the long-established
work on anisotropic diffusion in image processing, we present a novel
edge-preserving diffusion model that is a generalization of denoising diffusion
probablistic models (DDPM). In particular, we introduce an edge-aware noise
scheduler that varies between edge-preserving and isotropic Gaussian noise. We
show that our model's generative process converges faster to results that more
closely match the target distribution. We demonstrate its capability to better
learn the low-to-mid frequencies within the dataset, which plays a crucial role
in representing shapes and structural information. Our edge-preserving
diffusion process consistently outperforms state-of-the-art baselines in
unconditional image generation. It is also more robust for generative tasks
guided by a shape-based prior, such as stroke-to-image generation. We present
qualitative and quantitative results showing consistent improvements (FID
score) of up to 30% for both tasks. We provide source code and supplementary
content via the public domain edge-preserving-diffusion.mpi-inf.mpg.de .