Writing study: High-accuracy and dimension-free sampling with diffusions
← ICML 2026 oral writing corpus
Khashayar Gatmiry, Sitan Chen, Adil Salim · Official ICML 2026 oral record
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
- 33 physical pages
- Before references / appendix
- ≈ 7.89 page-equivalents
- Main figures / tables
- 0 / 0
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- ≈ 21.91 page-equivalents
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 | ≈ 2.39 pp. | 7.24% |
| 2. Preliminaries and our algorithm | 3 | ≈ 2.13 pp. | 6.45% |
| 3. Overview of proof | 5 | ≈ 2.79 pp. | 8.45% |
| 4. Outlook | 8 | ≈ 0.22 pp. | 0.67% |
| Impact statement | 8 | ≈ 0.05 pp. | 0.15% |
| References | 8 | ≈ 3.2 pp. | 9.7% |
| A. Further related work | 12 | ≈ 0.38 pp. | 1.15% |
| B. Notation | 12 | ≈ 0.8 pp. | 2.42% |
| C. Derivative calculations | 13 | ≈ 4.83 pp. | 14.64% |
| D. Proof of Lemma 3.4 | 18 | ≈ 0.69 pp. | 2.09% |
| E. Proof of Theorem 3.5 | 18 | ≈ 5.83 pp. | 17.67% |
| F. Proof of Proposition 3.6 | 24 | ≈ 3.68 pp. | 11.15% |
| G. Proof of Theorem 3.7 | 28 | ≈ 2.13 pp. | 6.45% |
| H. Proof of Corollary 3.9 | 30 | ≈ 1.15 pp. | 3.48% |
| I. Upper estimates on the movement of the probability flow ODE | 31 | ≈ 2.44 pp. | 7.39% |
All detected figure and table locations
Main text
No recognized caption labels.
Attached appendix
No recognized caption labels.
Argument and organization
- 1 Introduction and contributions; 1.2 Related work
Motivates the accuracy-dependence gap and states distributional and oracle assumptions beside the principal guarantee.
- 2 Preliminaries and our algorithm
Explains why small-step discretization is not the only perspective, then develops collocation and nested sampler pseudocode.
- 3 Overview of proof; 4 Outlook
Orders the proof ingredients from low-degree approximation to algorithm trajectory and sampler convergence before naming open extensions.
Problem, claim and contribution
The title advantage is unpacked as polylogarithmic accuracy dependence and dimension entering through support radius rather than as a generic claim of efficient generation.
Abstract and Section 1.1, pp.1-2 · Main paper
Argument and section order
A roadmap names the sampler construction and the structural result needed by the proof, letting the reader distinguish intuition from the deferred derivations.
Section 1.3, p.3; Section 3 opening, p.5 · Main paper
Figures, captions and visual explanation
The inspected theory pages use theorem/assumption typography and two compact algorithms instead of a decorative architecture figure; the inner solver and outer sampler have separate inputs and outputs.
Theorem 1.1, p.2; Algorithms 1-2, p.5 · Main paper
Tables, comparisons and evidence
The convergence presentation distinguishes Wasserstein and total-variation guarantees and explains the score-error and postprocessing differences rather than comparing only a headline rate.
Section 3.3 and Theorem 3.7, p.7; Corollary 3.9, p.8 · Main paper
Appendix and reproducibility
The appendix first provides further related work and notation before proof-specific sections; the notation page explicitly warns about its time-index convention.
Appendices A-B, p.12; main roadmap, p.3 · Main paper
Clarity and writing conventions
The related-work discussion calls several bounds incomparable and explains which parameters improve or worsen, preserving trade-offs in a priority-focused introduction.
Section 1.2, pp.2-3; Outlook, p.8 · Main paper
What to reuse—and what not to infer
Transferable lesson: For a theory contribution, expose the assumption/oracle contract and the route from structural lemma to algorithm guarantee before the full proof.
Boundary: Dimension-free wording is qualified by support radius and hidden logarithmic factors; this writing scan is not proof verification or evidence of practical runtime gains.
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.8, with focused physical-page text inspection on 1, 2, 3, 4, 5, 6, 7, 8. 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 12. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.
- Visually inspected PDF pages
- 2, 5
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.