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

• URL: http://arxiv.org/abs/2605.26032v1
• Date: Mon, 25 May 2026 17:01:21 GMT
• Title: Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution
• Abstract summary: Creating images from noise is image generation; reconstructing fine details from coarse inputs is super-resolution.<n>We introduce $textbfSKILD$, a model that unifies generation and continuous super-resolution within a single unconditional framework.<n> Empirically, SKILD reaches FID $2.65$ and Inception Score $9.63$ on unconditional CIFAR-10, performs $2times$--$8times$ super-resolution on ImageNet from a single unconditional checkpoint.
• Score: 27.232771005158146
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\textbf{SKILD}$, a $\textbf{S}$cale-invariant $\textbf{K}$-Space $\textbf{I}$mage $\textbf{L}$earning $\textbf{D}$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: $\textit{no task-specific architecture, no conditioning branch, no classifier-free guidance, no retraining per scale factor}$. Empirically, SKILD reaches FID $2.65$ and Inception Score $9.63$ on unconditional CIFAR-10, performs $2\times$--$8\times$ 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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