Scale Space Diffusion

TL;DR

This paper introduces Scale Space Diffusion, a novel diffusion model that incorporates scale-space theory to process images at multiple resolutions, reducing computational complexity while maintaining quality.

Contribution

It formalizes the connection between diffusion models and scale-space theory, proposing a new framework and a specialized UNet variant for resolution-efficient image generation.

Findings

Scale Space Diffusion performs comparably to traditional models on CelebA and ImageNet.

The model effectively handles resolution scaling and network depth variations.

Downsampling as degradation reduces computational load without sacrificing quality.

Abstract

Diffusion models degrade images through noise, and reversing this process reveals an information hierarchy across timesteps. Scale-space theory exhibits a similar hierarchy via low-pass filtering. We formalize this connection and show that highly noisy diffusion states contain no more information than small, downsampled images - raising the question of why they must be processed at full resolution. To address this, we fuse scale spaces into the diffusion process by formulating a family of diffusion models with generalized linear degradations and practical implementations. Using downsampling as the degradation yields our proposed Scale Space Diffusion. To support Scale Space Diffusion, we introduce Flexi-UNet, a UNet variant that performs resolution-preserving and resolution-increasing denoising using only the necessary parts of the network. We evaluate our framework on CelebA and ImageNet and analyze its scaling behavior across resolutions and network depths. Our project website ( https://prateksha.github.io/projects/scale-space-diffusion/ ) is available publicly.