Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution
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 SKILD, a Scale-invariant K-Space Image Learning Diffusion 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: no task−specific architecture, no conditioning branch, no classifier−free guidance, no retraining per scale factor. Empirically, SKILD reaches FID $2.61$ and Inception Score $9.65$ on unconditional CIFAR-10, performs 2×--8× 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.
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BibTeX
@misc{chen2026everything,
title = {{Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution}},
author = {Zixin Jessie Chen and Zhuo Chen and Archer Wang and Jeff Gore and William T. Freeman and Congyue Deng and Marin Soljačić},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.26032},
eprint = {2605.26032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.26032},
}
RIS
TY - UNPB
TI - Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution
AU - Zixin Jessie Chen
AU - Zhuo Chen
AU - Archer Wang
AU - Jeff Gore
AU - William T. Freeman
AU - Congyue Deng
AU - Marin Soljačić
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2605.26032
UR - https://arxiv.org/abs/2605.26032
AB - 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 SKILD, a Scale-invariant K-Space Image Learning Diffusion 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: no task−specific architecture, no conditioning branch, no classifier−free guidance, no retraining per scale factor. Empirically, SKILD reaches FID $2.61$ and Inception Score $9.65$ on unconditional CIFAR-10, performs 2×--8× 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.
ER -