Edge-preserving noise for diffusion models

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.