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

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← ICML 2026 oral writing corpus

Binxu Wang, Jacob A Zavatone-Veth, Cengiz Pehlevan · Official ICML 2026 oral record

Observed writing choices, not acceptance rules. This study examines the inspected manuscript version. It does not establish why the paper was accepted or that its presentation choices should be copied unchanged.

Figure, table and section ledger

Editorial contribution type: Theory & formal analysis (primary).

Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.

Canonical PDF

52 physical pages

Before references / appendix

≈ 8.8 page-equivalents

Main figures / tables

5 / 0

Attached appendix figures / tables

33 / 0

Attached appendix span

≈ 40.91 page-equivalents

Before references / appendix: ≈ 16.92%References / intervening material: ≈ 4.4%Attached appendix: ≈ 78.67%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Include the actual post-reference Contents page12 in the supporting-material envelope and join wrapped main headings.

Section-by-section lengths and source pages

The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.

Top-level heading	Starts on PDF page	Estimated span	Share of entire PDF
1. Introduction	1	≈ 0.79 pp.	1.52%
2. Notation and Set up	2	≈ 1 pp.	1.92%
3. Motivating Empirical Observation	3	≈ 0.47 pp.	0.9%
4. Theory of Diffusion Consistency Across Independent Data	3	≈ 2.02 pp.	3.88%
5. Consistency of Diffusion Samples for Linear Denoisers	5	≈ 1.65 pp.	3.17%
6. Validating Predictions on Deep Networks	7	≈ 0.86 pp.	1.65%
7. Discussion	8	≈ 1.21 pp.	2.33%
Impact Statement	9	≈ 0.05 pp.	0.1%
Acknowledgments	9	≈ 0.13 pp.	0.25%
References	9	≈ 2.29 pp.	4.4%
Contents	12	≈ 1 pp.	1.92%
A. Extended Related Work	13	≈ 1 pp.	1.92%
B. Extended Results and Figures	14	≈ 20 pp.	38.46%
C. Proofs and Derivations	34	≈ 16 pp.	30.77%
D. Experimental Details	50	≈ 2.74 pp.	5.27%
E. Usage of LLMs	52	≈ 0.18 pp.	0.35%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 4
• Figure 3 · p. 6
• Figure 4 · p. 6
• Figure 5 · p. 8

Attached appendix

• Figure 6 · p. 14
• Figure 7 · p. 14
• Figure 8 · p. 15
• Figure 9 · p. 15
• Figure 10 · p. 16
• Figure 11 · p. 16
• Figure 12 · p. 17
• Figure 13 · p. 18
• Figure 14 · p. 19
• Figure 15 · p. 20
• Figure 16 · p. 20
• Figure 17 · p. 21
• Figure 18 · p. 22
• Figure 19 · p. 23
• Figure 20 · p. 24
• Figure 21 · p. 25
• Figure 22 · p. 26
• Figure 23 · p. 26
• Figure 24 · p. 27
• Figure 25 · p. 27
• Figure 26 · p. 28
• Figure 27 · p. 28
• Figure 28 · p. 28
• Figure 29 · p. 29
• Figure 30 · p. 29
• Figure 31 · p. 29
• Figure 32 · p. 29
• Figure 33 · p. 30
• Figure 34 · p. 30
• Figure 35 · p. 30
• Figure 36 · p. 31
• Figure 37 · p. 32
• Figure 38 · p. 33

Argument and organization

1. 1 Introduction; 2 Preliminaries; 3 Motivating Empirical Observation

   Defines cross-split consistency and establishes a Gaussian linear baseline.

2. 4 Theory of Diffusion Consistency; 5 Consistency of Diffusion Samples

   Separates expectation and fluctuation for denoisers, then extends the analysis to sampling maps.

3. 6 Validating Predictions on Deep Networks; 7 Discussion

   Tests directional predictions in a non-memorization regime and delineates nonlinear departures.

Problem, claim and contribution

The paper asks why independently trained models map matched noise seeds to similar outputs, using shared first and second moments as a tractable baseline.

Introduction, p.1; motivating experiment, p.3 · Main paper

Argument and section order

Repeated expectation/fluctuation organization links the denoiser analysis to the full sampling-map analysis, with interpretation paragraphs after propositions.

Sections 4-5, pp.4-7 · Main paper

Figures, captions and visual explanation

A theory roadmap precedes noise-renormalization and shrinkage plots; a six-panel validation figure aligns generated examples, nearest-neighbor checks, spectral effects and seed-wise correlation.

Figure 2, p.4; Figure 5, p.8 · Main paper

Tables, comparisons and evidence

Deep-network validation distinguishes memorization from the regime where directional predictions correlate, and explicitly says absolute variability exceeds the linear prediction.

Sections 6-7, pp.7-8 · Main paper

Appendix and reproducibility

Counterfactual data splits perturb mean and covariance, while numerical details explain root-finding and quadrature needed to evaluate the analytical expressions.

Appendix B.2, p.18; Appendix D.1, p.50 · Main paper

Clarity and writing conventions

Approximation notation and the fixed empirical-mean assumption are stated with the propositions, and finite initial-noise corrections are separately signposted.

Proposition 4.1 and footnote, p.4; Section 5.1, p.6 · Main paper

What to reuse—and what not to infer

Transferable lesson: Separate an exact tractable model, its asymptotic approximations and its qualitative transfer to a richer model, with matching visual and numerical checks for each layer.

Boundary: The theory fixes the mean to isolate covariance effects and uses a linear/asymptotic setting; the deep-network correlations are regime-dependent and do not certify absence of memorization or equal variance magnitudes.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-07

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 3, 4, 5, 6, 7, 8, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.

Appendix / supplement

Appendix organization and main-text pointers were checked; focused text inspection of physical pages 13, 18, 20, 30, 34, 50. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

4, 8

This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.

• Published proceedings PDF, PMLR volume 306, retrieved 2026-10-07 · 52 pages