Writing study: Half-order Fine-Tuning for Diffusion Model: A Recursive Likelihood Ratio Optimizer

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← ICLR 2026 oral writing corpus

Tao Ren, Zishi Zhang, Jinyang Jiang, Zehao Li, Shentao Qin, Yi Zheng, Guanghao Li, Qianyou Sun, Yan Li, Jiafeng Liang, Xinping Li, Yijie Peng · 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: Learning & optimization algorithms (primary) · Inference, algorithms & systems efficiency.

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

27 physical pages

Before references / appendix

≈ 9.2 page-equivalents

Main figures / tables

6 / 5

Attached appendix figures / tables

5 / 5

Attached appendix span

≈ 12.89 page-equivalents

Before references / appendix: ≈ 34.07%References / intervening material: ≈ 18.19%Attached appendix: ≈ 47.74%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	2	≈ 1.36 pp.	5.04%
2 RELATED WORK	3	≈ 0.2 pp.	0.74%
3 UNBIASED MINIMAL VARIANCE GRADIENT ESTIMATOR FOR DIFFUSION	3	≈ 1.14 pp.	4.22%
4 SOLVING THE VARIANCE MINIMIZATION PROBLEM: RECURSIVE	4	≈ 1.57 pp.	5.81%
5 EXPERIMENTS	6	≈ 2.3 pp.	8.52%
6 THEORETICAL PROPERTIES OF GRADIENT ESTIMATORS: BIAS, VARIANCE,	8	≈ 1.08 pp.	4%
7 CONCLUSION	9	≈ 0.34 pp.	1.26%
ACKNOWLEDGMENTS	10	≈ 0.09 pp.	0.33%
REFERENCES	10	≈ 4.91 pp.	18.19%
A EXTENDED RELATED WORKS	15	≈ 0.49 pp.	1.81%
B EXPERIMENTS SETTINGS	15	≈ 2.11 pp.	7.81%
C HYPEPARAMETERS	17	≈ 0.41 pp.	1.52%
D QUALITATIVE RESULTS OF TEXT2IMAGE	18	≈ 1 pp.	3.7%
E QUALITATIVE RESULTS OF TEXT2VIDEO	19	≈ 1 pp.	3.7%
F DETAILS FOR DIFFUSIVE CHAIN-OF-THOUGHT EXPERIMENT	20	≈ 1.3 pp.	4.81%
G MEMORY PROFILE, TIME COMPLEXITY, AND DIFFERENT DIFFUSION	21	≈ 0.89 pp.	3.3%
H ABLATIONS ON THE SUB-CHAIN LENGTH h	22	≈ 0.35 pp.	1.3%
I MORE RESULTS ON VBENCH	22	≈ 0.87 pp.	3.22%
J PROOFS	23	≈ 4.49 pp.	16.63%

All detected figure and table locations

Main text

• Figure 1 · p. 1
• Figure 2 · p. 2
• Figure 3 · p. 2
• Figure 4 · p. 3
• Table 1 · p. 4
• Table 2 · p. 6
• Table 3 · p. 6
• Figure 5 · p. 7
• Figure 6 · p. 7
• Table 4 · p. 8
• Table 5 · p. 8

Attached appendix

• Figure 7 · p. 18
• Figure 8 · p. 19
• Figure 9 · p. 20
• Figure 10 · p. 20
• Figure 11 · p. 21
• Table 6 · p. 21
• Table 7 · p. 21
• Table 8 · p. 22
• Table 9 · p. 22
• Table 10 · p. 23

Argument and organization

1. Estimator design space

   Explains the memory–bias–variance tradeoff before introducing the hybrid estimator.

2. RLR and diffusion experiments

   Pairs local-gradient design with image/video reward experiments and a restricted prompt-decomposition demonstration.

3. Theory and implementation appendix

   Separates regularity assumptions, estimator proofs, memory/time accounting and sampler settings.

Problem, claim and contribution

The opening compares full differentiation, truncated differentiation and policy gradients as competing resource tradeoffs; this gives the hybrid design an intelligible motivation before its equations.

Sections 1 and 3, pages 1–4 · Main paper

Argument and section order

The paper first defines the recursive generation process, then narrows a large estimator design space to a local half-order subchain plus zeroth-order and direct terms.

Sections 3–4, pages 3–5 · Main paper

Figures, captions and visual explanation

Figure 4 overlays a symbolic denoising chain and image examples, using separate arrows for forward computation, perturbation and differentiation. The legend makes the three gradient-estimation regions readable.

Figure 4, page 3 · Main paper

Tables, comparisons and evidence

The appendix distinguishes per-step speed from time to reach a common aesthetic score and reports host RAM separately from GPU memory. Those are more informative comparisons than an isolated memory-saving percentage.

Appendix G, Tables 6–7, page 21 · Main paper

Appendix and reproducibility

A contents page routes readers to hyperparameters, prompt templates, qualitative samples, solver checks, subchain ablations and proofs. The same-score timing and longer-subchain costs belong near the main efficiency claim.

Appendix contents page 14; Appendices C and G–J · Main paper

Clarity and writing conventions

Some theoretical statements need narrower wording: the perturbation proof concerns its explicitly randomized process, and the variance appendix's claim that the direct term has zero variance is not a general consequence of having no injected parameter noise.

Appendix J.3–J.4, pages 24–26 · Main paper

What to reuse—and what not to infer

Transferable lesson: Make an optimizer's tradeoff concrete with one computation-graph legend and a table separating peak device memory, host memory, step time and time to a common target.

Boundary: Do not repeat an unconditional minimum-variance or unbiased-for-the-unperturbed-model claim. The proof uses a perturbed recursion, regularity assumptions and a restricted estimator construction; automatic reward gains are not a human preference study.

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

Pages 1–9, Sections 1–7; reference list on pages 10–13 checked for source organization

Appendix / supplement

Pages 14–27, contents and Appendices A–J including all proof and resource tables

Visually inspected PDF pages

3, 21

• ICLR 2026 final proceedings · 27 pages