pages/conclusion/page.md

# Conclusion


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This reproduction verified all 5 claims from the official challenge for "A Random Matrix Perspective on the Consistency of Diffusion Models" (arXiv 2602.02908, ICML 2026 Oral).

Claims 1-4 (the paper's closed-form theory: linear consistency prediction, self-consistency renormalization, factorized variance law, and fractional matrix power extension to sampling trajectories) were verified numerically against Monte Carlo simulation, with Claim 2 additionally cross-checked against the authors' own released code.

Claim 5 (deep network validation) was tested at two scales: a small MLP on real MNIST confirmed the qualitative consistency pattern, and a more thorough UNet trained on real CIFAR10 across four dataset sizes tested all three of the paper's stated predictions directly -- consistency vs. a genuine linear-diffusion baseline, overshrinkage of low-variance eigenmodes, and eigenmode-dependent anisotropic cross-split deviation. All four sub-checks were directionally consistent with the paper's predictions.

Reproducibility notes: every empirical claim was run as a real, independently-verifiable Hugging Face Job with public execution logs rather than local/offline runs. The main scope reduction versus the paper is Claim 5, which uses far less compute than the paper's full setup (7 datasets, UNet+DiT, 50k training steps per run) -- this reproduction used 1 dataset, 1 architecture, and up to 4000 steps per run.