Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution

arXiv:2605.26032v1 Announce Type: cross Abstract: Creating images from noise is image generation; reconstructing fine details from coarse inputs is super-resolution. Despite their practical differences, both can be understood as reversing information loss across scales. We introduce extbf{SKILD}, a extbf{S}cale-invariant extbf{K}-Space extbf{I}mage extbf{L}earning extbf{D}iffusion model that unifies generation and continuous super-resolution within a single unconditional framework. Both natural images and critical physical systems exhibit scale invariance, and we leverage it to design a forward process that attenuates image content from fine to coarse scales while injecting spectrum-matched Gaussian noise, making scale an explicit coordinate of the diffusion dynamics. The same trained reverse process performs generation and continuous super-resolution by varying only the starting timestep: extit{no task-specific architecture, no conditioning branch, no classifier-free guidance, no retraining per scale factor}. Empirically, SKILD reaches FID 2.65 and Inception Score 9.63 on unconditional CIFAR-10, performs 2imes--8imes super-resolution on ImageNet from a single unconditional checkpoint while outperforming conditional models across perceptual metrics, and reconstructs critical Ising models whose connected four-point correlations closely track the ground truth.

Source: arXiv cs.AI | 2026-05-26