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| { | |
| "schema_version": 1, | |
| "title": "Reproduction: A theory of learning data statistics in diffusion models, from easy to hard", | |
| "emoji": "🌀", | |
| "space_id": "snaykey/repro-embedding-defense", | |
| "paper": { | |
| "arxiv_id": "2603.12901", | |
| "openreview_id": "xPdpfcJ65T" | |
| }, | |
| "tags": [ | |
| "icml2026-repro", | |
| "paper-xPdpfcJ65T" | |
| ], | |
| "updated_at": "2026-07-28T00:00:00+00:00", | |
| "root": { | |
| "slug": "index", | |
| "title": "Reproduction: A theory of learning data statistics in diffusion models, from easy to hard", | |
| "file": "pages/index.md", | |
| "children": [ | |
| { | |
| "slug": "executive-summary", | |
| "title": "Executive summary", | |
| "file": "pages/executive-summary/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-1-figure-1-distributional-simplicity-bias", | |
| "title": "Diffusion denoisers trained on natural images exhibit a distributional simplicity bias: on CIFAR-10, a U-Net achieves nearly identical test loss on real images versus Gaussian clones matched in mean and covariance for roughly 10^3 training steps before performance diverges, indicating pair-wise statistics are learned first (Figure 1).", | |
| "file": "pages/claim-1-figure-1-distributional-simplicity-bias/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-2-proposition-4-3-sample-complexity-threshold", | |
| "title": "For a k-th order cumulant target, the sample complexity threshold for weak recovery via projected gradient descent is n_hat(d,k) = omega(d^(k-1) log^2 d), with |v . w(n_hat)| approaching 1 as d approaches infinity after this many steps (Proposition 4.3).", | |
| "file": "pages/claim-2-proposition-4-3-sample-complexity-threshold/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-3-proposition-4-4-negative-result", | |
| "title": "If the number of samples n(d) = o(n_hat(d,k*)), standard SGD provably fails to achieve weak recovery of the k*-th cumulant, establishing a sharp learnable/unlearnable sample-complexity separation (Proposition 4.4).", | |
| "file": "pages/claim-3-proposition-4-4-negative-result/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-4-proposition-4-6-independent-latents", | |
| "title": "In a mixed-cumulant latent model, pair-wise statistics are recoverable with linear sample complexity n = Theta(d * polylog(d)), while recovering the fourth cumulant requires Omega(d^3) samples when latent variables are independent (Proposition 4.6).", | |
| "file": "pages/claim-4-proposition-4-6-independent-latents/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-5-proposition-4-6-correlated-latents", | |
| "title": "When latent variables underlying the pair-wise and higher-order statistics are positively correlated, the fourth-cumulant recovery sample complexity accelerates from cubic to linear in d (Proposition 4.6).", | |
| "file": "pages/claim-5-proposition-4-6-correlated-latents/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-6-proposition-4-7-spherical-constraint", | |
| "title": "Unconstrained SGD exhibits contraction dynamics toward w=0 for many activation functions, causing learning failure, whereas constraining updates to the unit sphere (spherical projection) preserves the ability to learn higher-order statistics (Proposition 4.7).", | |
| "file": "pages/claim-6-proposition-4-7-spherical-constraint/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "conclusion", | |
| "title": "Conclusion", | |
| "file": "pages/conclusion/page.md", | |
| "children": [] | |
| } | |
| ] | |
| } | |
| } |