Writing study: Quotient-Space Diffusion Models

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← ICLR 2026 oral writing corpus

Yixian Xu, Yusong Wang, Shengjie Luo, Kaiyuan Gao, Tianyu He, Di He, Chang Liu · Official ICLR 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 foundations (primary) · Learning & optimization algorithms.

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

43 physical pages

Before references / appendix

≈ 9.21 page-equivalents

Main figures / tables

3 / 3

Attached appendix figures / tables

0 / 0

Attached appendix span

≈ 27.89 page-equivalents

Before references / appendix: ≈ 21.42%References / intervening material: ≈ 13.72%Attached appendix: ≈ 64.86%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

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	≈ 1.88 pp.	4.37%
2 BACKGROUND	3	≈ 1.18 pp.	2.74%
3 METHODS	4	≈ 4.24 pp.	9.86%
4 EXPERIMENTS	8	≈ 1.35 pp.	3.14%
References	10	≈ 0.45 pp.	1.05%
5 CONCLUSION	10	≈ 0.45 pp.	1.05%
ACKNOWLEDGMENTS	11	≈ 0.09 pp.	0.21%
6 ETHICS STATEMENT	11	≈ 0.1 pp.	0.23%
7 REPRODUCIBILITY STATEMENT	11	≈ 0.14 pp.	0.33%
8 THE USE OF LARGE LANGUAGE MODELS (LLMS)	11	≈ 0.11 pp.	0.26%
REFERENCES	11	≈ 4.56 pp.	10.6%
APPENDIX	16	≈ 0.12 pp.	0.28%
A RELATED WORK	16	≈ 1.03 pp.	2.4%
B BACKGROUND IN RIEMANNIAN GEOMETRY AND STOCHASTIC CALCULUS	17	≈ 4.13 pp.	9.6%
C LIE GROUP AND QUOTIENT SPACE	21	≈ 4.84 pp.	11.26%
D PROOFS	26	≈ 9.39 pp.	21.84%
E TRAINING AND SAMPLING METHODS IN MORE GENERAL CASES	35	≈ 0.91 pp.	2.12%
F EXPERIMENTAL DETAILS	36	≈ 3.11 pp.	7.23%
G ADDITIONAL EXPERIMENTAL RESULTS AND DISCUSSIONS	39	≈ 4.37 pp.	10.16%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Table 1 · p. 3
• Figure 2 · p. 4
• Figure 3 · p. 8
• Table 2 · p. 9
• Table 3 · p. 10

Attached appendix

No recognized caption labels.

Argument and organization

1. Introduction / Background

   Explains symmetry redundancy with a toy process before introducing quotient geometry.

2. Methods

   Moves from general projection/lifting theorems to molecular shape space, objectives and samplers.

3. Comparative analysis / Experiments

   Connects a mechanistic taxonomy to matched-backbone empirical comparisons.

4. Appendices A–G

   Supplies prerequisite mathematics, proofs, algorithms, experimental details and extensions.

Problem, claim and contribution

Figure 1 demonstrates the central distinction before dense geometry: eliminate rotational wandering while preserving the endpoint distribution. Table 1 then separates learning redundancy from sampler compatibility, making the comparison criteria explicit.

Figure 1, p.2; Table 1, p.3 · Main paper

Argument and section order

The derivation first projects to an abstract quotient and then lifts back to implementable coordinates. Only afterward does the paper instantiate molecular shape space and give the training loss, avoiding an unexplained algorithm-first presentation.

§§3.1–3.3, pp.4–7 · Main paper

Figures, captions and visual explanation

Table 2 separates datasets, recall/precision, mean/median and architecture families; reproduced baselines are labeled separately from published numbers. Table 3 likewise separates stochastic noise settings from deterministic sampling.

Tables 2–3, pp.9–10 · Main paper

Tables, comparisons and evidence

The footnote acknowledges changed ET-Flow preprocessing. A second footnote excludes potentially corrupted FoldSeek metrics; Appendix F names the fixed version and limits its re-evaluation to available matched models.

p.9 footnote 1; p.10 footnote 2; Appendix F.2.5, p.39 · Main paper

Appendix and reproducibility

The appendix begins with a navigation paragraph, then develops prerequisites before proofs. Algorithms 1–3 expose training/sampling variants; near-collinear numerical regularization and transition-density limitations receive dedicated discussion.

p.16; Appendix E, pp.35–36; G.1 and G.5, pp.39–43 · Main paper

Clarity and writing conventions

Broad superiority language should be narrowed to matched settings and named metrics: the QM9 precision-coverage column favors GeoDiff alignment over quotient diffusion, while other columns favor the latter.

§4.1 and Table 2, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Pair a small conceptual figure with a mechanistic comparison table, then present empirical results with explicit baseline provenance and evaluation-tool versions.

Boundary: The source has an unresolved curvature-sign inconsistency: Theorem 4/Eq.9 uses a negative correction, whereas Eq.12 and Algorithm 3 use a positive correction for the same named field. Do not publish executable SDE guidance without resolving it.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-19

Reading status

Full text + selected visuals inspected

Main text

PDF pp.1–10, abstract and §§1–5; statements and references pp.11–15

Appendix / supplement

PDF pp.16–43, Appendices A–G including geometry definitions, all stated proofs, samplers, protocols and metric-version discussion

Visually inspected PDF pages

2, 6, 7, 9, 10

• official ICLR 2026 proceedings PDF · 43 pages