{
  "schema_version": 1,
  "title": "Repro - A theory of learning data statistics in diffusion models, from easy to hard",
  "emoji": "🎯",
  "space_id": "agharsallah/xpdpfcj65t-logbook",
  "paper": {
    "arxiv_id": null,
    "openreview_id": "xPdpfcJ65T",
    "icml_id": "60700",
    "title": "A theory of learning data statistics in diffusion models, from easy to hard",
    "forum": "https://openreview.net/forum?id=xPdpfcJ65T"
  },
  "tags": [
    "icml2026-repro",
    "paper-xPdpfcJ65T"
  ],
  "updated_at": "2026-07-21T11:04:07+00:00",
  "root": {
    "slug": "index",
    "title": "Repro - A theory of learning data statistics in diffusion models, from easy to hard",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "overview-method",
        "title": "Overview & Method",
        "file": "pages/overview-method/page.md",
        "children": []
      },
      {
        "slug": "claim-1-diffusion-denoisers-trained-on-natural-image",
        "title": "Claim 1: Diffusion denoisers trained on natural image",
        "file": "pages/claim-1-diffusion-denoisers-trained-on-natural-image/page.md",
        "children": []
      },
      {
        "slug": "claim-2-for-a-k-th-order-cumulant-target-the-sample",
        "title": "Claim 2: For a k-th order cumulant target, the sample",
        "file": "pages/claim-2-for-a-k-th-order-cumulant-target-the-sample/page.md",
        "children": []
      },
      {
        "slug": "claim-3-if-the-number-of-samples-n-d-o-n-hat-d-k",
        "title": "Claim 3: If the number of samples n(d) = o(n_hat(d,k*",
        "file": "pages/claim-3-if-the-number-of-samples-n-d-o-n-hat-d-k/page.md",
        "children": []
      },
      {
        "slug": "claim-4-in-a-mixed-cumulant-latent-model-pair-wise",
        "title": "Claim 4: In a mixed-cumulant latent model, pair-wise",
        "file": "pages/claim-4-in-a-mixed-cumulant-latent-model-pair-wise/page.md",
        "children": []
      },
      {
        "slug": "claim-5-when-latent-variables-underlying-the-pair-wi",
        "title": "Claim 5: When latent variables underlying the pair-wi",
        "file": "pages/claim-5-when-latent-variables-underlying-the-pair-wi/page.md",
        "children": []
      },
      {
        "slug": "claim-6-unconstrained-sgd-exhibits-contraction-dynam",
        "title": "Claim 6: Unconstrained SGD exhibits contraction dynam",
        "file": "pages/claim-6-unconstrained-sgd-exhibits-contraction-dynam/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 7390,
  "revision": "1784631847787499000"
}