| # 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 |
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| 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** | |
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| 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) |
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|
| **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. |
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|
| **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 |
|
|
| ```bash |
| pip install -r requirements.txt |
| python run_repro.py # default config, ~20 s |
| python run_repro.py --config configs/repro.yaml |
| ``` |
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|
| 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 |
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|
| - `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). |
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| ## Method notes |
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|
| - 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. |
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