{
  "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 $2.61$ and Inception Score $9.65$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.26032",
  "author_total": 7,
  "authors": [
    {
      "name": "Zixin Jessie Chen"
    },
    {
      "name": "Zhuo Chen"
    },
    {
      "name": "Archer Wang"
    },
    {
      "name": "Jeff Gore"
    },
    {
      "name": "William T. Freeman"
    },
    {
      "name": "Congyue Deng"
    },
    {
      "name": "Marin Soljačić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48cqtvggrpa6k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.26032",
  "fulltext_url": null,
  "id": "48cqtvggrpa6k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.26032",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "openalex",
      "1707|Generative Adversarial Networks and Image Synthesis"
    ]
  ],
  "openalex": "W7162415769",
  "pdf_url": "https://arxiv.org/pdf/2605.26032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48cqtvggrpa6k.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2605.26032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.26032"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution",
  "title_text": "Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:33Z",
  "url": "https://research.draconitic.com/paper/48cqtvggrpa6k",
  "venue": "arXiv",
  "versions": []
}