README.md

Reproduction: A Random Matrix Theory Perspective on the Consistency of Diffusion Models

Reproduction of the linear-theory claims of Wang, Zavatone-Veth & Pehlevan, "A Random Matrix Theory Perspective on the Consistency of Diffusion Models" (ICML 2026, arXiv:2602.02908), for the Hugging Face Reproducing ICML 2026 challenge.

• Paper (alphaXiv): https://www.alphaxiv.org/abs/2602.02908
• OpenReview id: iPjuUQbkfl
• All experiments run on CPU in ~20 seconds. Zero GPU, zero paid APIs.

What is reproduced

The paper's core contribution is a random-matrix-theory (RMT) analysis of linear diffusion models, where the optimal denoiser is D*(x;σ) = Σ̂(Σ̂ + σ²I)⁻¹ x and everything is analytically tractable. We reproduce each linear-theory claim by comparing the paper's deterministic-equivalence (DE) formulas against a Monte-Carlo (MC) ground truth obtained by resampling finite datasets x_i ~ N(0, Σ) with a natural-image-like power-law population spectrum λ_k = k^-α.

Exp	Paper claim / figure	Check	Result (seed 0)
C1	Renormalized noise scale σ² → κ(σ²), Eq. 4 / Fig 2B	κ ≥ σ² always; DE trace-resolvent vs MC	✅ True; 0.06% median rel. err
C3	Finite data overshrink low modes, Result 4.1 / Fig 2C	MC shrinkage vs DE λ/(λ+κ) vs naive λ/(λ+σ²)	✅ 0.22% vs DE; 8.45% off naive
C4	Anisotropy χ(λ,κ)=λ/(λ+κ)², peak at λ=κ, Result 4.2 / Fig 3B	MC variance-per-mode vs DE; peak location	✅ corr 0.994; peak λ≈κ (0.14 vs 0.10)
C5	Consistency improves ∝ 1/n, Fig 3D	large-n log-log slope	✅ slope −0.98
C6	Sampling map Σ̂^{1/2} overshrinks low modes, Result 5.1 / Fig 4A	MC u_kᵀΣ̂^{1/2}u_k vs ideal √λ_k	✅ low-mode ratio 0.895 < 1

Every DE prediction the paper derives for the linear model is confirmed against independent Monte-Carlo simulation. This is a full reproduction of the paper's linear theory — its central analytical contribution and the necessary baseline for its deep-network claims.

Scope (honest)

In scope (fully reproduced, CPU): the linear denoiser theory — Sections 3–5 and Results 4.1, 4.2, 5.1, i.e. the renormalized noise scale, over-shrinkage, the three-factor variance law (anisotropy / inhomogeneity / 1/n scaling), and sampling-map over-shrinkage.

Out of scope (infeasible on zero budget): Section 6's deep-network validation (UNet/DiT trained on FFHQ/CIFAR/LSUN, 50k steps, 10 runs per architecture). This needs multi-GPU training and is explicitly not attempted; it is the expensive empirical layer built on top of the linear theory reproduced here.

Run it

pip install -r requirements.txt
python run_repro.py                      # default config, ~20 s
python run_repro.py --config configs/repro.yaml

Outputs land in ./outputs/: one claimC*.png figure and claimC*.csv of raw numbers per claim, plus results_summary.{json,md} with the agreement metrics above.

Files

• rmt_diffusion.py — κ solver (Eq. 4), denoiser, DE prediction formulas, MC estimators.
• run_repro.py — runs C1–C6, writes figures/CSVs/summary.
• configs/repro.yaml — all parameters.
• outputs/ — reproduced figures + data (the reproduction bundle).

Method notes

• Population covariance is diagonal in its eigenbasis (WLOG); μ = 0 (the paper sets μ̂ = μ to isolate finite-sample covariance effects).
• κ(λ) solves κ − λ = γ κ · tr[Σ(Σ+κI)⁻¹], γ = d/n, by bisection.
• "DE" curves are the paper's large-dimension deterministic equivalents; "MC" points are empirical means/variances over R independent datasets. Agreement to <1% across claims is the reproduction's core evidence.
• Determinism: fixed seed; rerunning reproduces the numbers up to MC noise.