Writing study: High-Accuracy Sampling for Diffusion Models and Log-Concave Distributions
← ICML 2026 oral writing corpus
Fan Chen, Sinho Chewi, Constantinos Costis Daskalakis, Alexander Rakhlin · 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
- 35 physical pages
- Before references / appendix
- ≈ 8.12 page-equivalents
- Main figures / tables
- 0 / 0
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- ≈ 23.91 page-equivalents
Source-bound correction: Restore the post-reference Contents page and Appendix A-F from source-text glyph positions on physical pp12-34. Appendix A starts below the table of contents on p12; the supporting-material envelope starts at Contents, not at the first proof. This is not an absent appendix.
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 | ≈ 2.17 pp. | 6.2% |
| 2. Background on Diffusion Models | 3 | ≈ 0.63 pp. | 1.8% |
| 3. Key Subroutine: Gaussian Tilts | 4 | ≈ 1.77 pp. | 5.06% |
| 4. Diffusion Sampling | 5 | ≈ 2.05 pp. | 5.86% |
| 5. Application to Log-Concave Sampling | 7 | ≈ 0.78 pp. | 2.23% |
| 6. Conclusion | 8 | ≈ 0.27 pp. | 0.77% |
| Impact Statement | 8 | ≈ 0.13 pp. | 0.37% |
| Acknowledgments | 9 | ≈ 0.08 pp. | 0.23% |
| References | 9 | ≈ 2.96 pp. | 8.46% |
| Contents | 12 | ≈ 0.65 pp. | 1.86% |
| A. Discussion | 12 | ≈ 0.62 pp. | 1.77% |
| B. Additional Notation and Technical Tools | 13 | ≈ 4.87 pp. | 13.91% |
| C. Proof of Theorem 3.1 | 18 | ≈ 0.51 pp. | 1.46% |
| D. Proofs for Section 3 | 18 | ≈ 1.55 pp. | 4.43% |
| E. Proofs for Section 4 | 20 | ≈ 14.11 pp. | 40.31% |
| F. Log-Concave Sampling | 34 | ≈ 1.6 pp. | 4.57% |
All detected figure and table locations
Main text
No recognized caption labels.
Attached appendix
No recognized caption labels.
Argument and organization
- 1 Introduction; 2 Background
States the oracle-complexity question, error metric and three assumption regimes.
- 3 Gaussian Tilts; 4 Diffusion Sampling
Builds a first-order rejection subroutine and specializes it to progressively structured distributions.
- 5 Log-Concave Sampling; 6 Conclusion
Transfers the subroutine through a proximal sampler and distinguishes theoretical gains from practical readiness.
Problem, claim and contribution
High accuracy refers to logarithmic target-error dependence in an oracle model, with score-estimation error separately retained rather than assumed away.
Abstract and Equation 1, p.1; contribution summary, p.2 · Main paper
Argument and section order
A one-dimensional rejection example motivates the general algorithm, followed by exact-oracle analysis and only then approximate-score diffusion results.
Section 3.1, p.4; Sections 3.2-4, pp.4-5 · Main paper
Figures, captions and visual explanation
The inspected theory pages use a compact ruled pseudocode block and boxed complexity expressions instead of illustrative figures; assumptions remain adjacent to each bound.
Algorithm 1, p.4; Theorems 4.4 and 4.7, p.7 · Main paper
Tables, comparisons and evidence
Dimension improvements are accompanied by explicitly worse score-error factors, and early-stopped distribution guarantees are distinguished from weaker-metric guarantees for the original data.
Background, p.3; discussion after Theorems 4.4 and 4.7, p.7 · Main paper
Appendix and reproducibility
The comparison with concurrent work calls the bounds incomparable and analyzes smoothing and score-tail assumptions before the technical proof sections.
Appendix A.1, p.13; Appendix E.1, p.20 · Main paper
Clarity and writing conventions
The conclusion explicitly says that multiple score calls and conservative step conditions leave competitive practical implementation unresolved.
Conclusion, p.8 · Main paper
What to reuse—and what not to infer
Transferable lesson: Present assumption regimes, oracle access, discrepancy metrics and approximation factors together so an asymptotic improvement cannot be mistaken for measured wall-clock acceleration.
Boundary: No empirical speed benchmark is supplied in the main manuscript; this writing scan does not independently validate the proofs or transfer the bounds to later arXiv revisions.
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, 5, 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, 20. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.
- Visually inspected PDF pages
- 4, 7
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.