Writing study: GLASS Flows: Efficient Inference for Reward Alignment of Flow and Diffusion Models

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← ICLR 2026 oral writing corpus

Peter Holderrieth, Uriel Singer, Tommi Jaakkola, Ricky T. Q. Chen, Yaron Lipman, Brian Karrer · 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: Inference, algorithms & systems efficiency (primary) · Theory & formal foundations.

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

≈ 10.11 page-equivalents

Main figures / tables

3 / 2

Attached appendix figures / tables

11 / 3

Attached appendix span

≈ 20.89 page-equivalents

Before references / appendix: ≈ 28.89%References / intervening material: ≈ 11.43%Attached appendix: ≈ 59.69%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 MIT CSAIL, 2FAIR, Meta	1	≈ 1.35 pp.	3.86%
2 BACKGROUND AND MOTIVATION	2	≈ 0.67 pp.	1.91%
3 MOTIVATION: EFFICIENT TRANSITIONS FOR REWARD ALIGNMENT	3	≈ 0.98 pp.	2.8%
4 GLASS FLOWS	4	≈ 3.38 pp.	9.66%
5 RELATED WORK	7	≈ 0.85 pp.	2.43%
6 EXPERIMENTS	8	≈ 2.29 pp.	6.54%
7 CONCLUSION	10	≈ 0.38 pp.	1.09%
REFERENCES	11	≈ 4 pp.	11.43%
A PROOFS	15	≈ 5 pp.	14.29%
B ADDITIONAL GLASS DISCUSSION	20	≈ 4.67 pp.	13.34%
C EXTENDED RELATED WORK	24	≈ 2.33 pp.	6.66%
D EXPERIMENTS	27	≈ 8.89 pp.	25.4%

All detected figure and table locations

Main text

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

Attached appendix

• Figure 4 · p. 27
• Figure 5 · p. 27
• Table 3 · p. 28
• Table 4 · p. 28
• Figure 6 · p. 28
• Figure 7 · p. 29
• Table 5 · p. 30
• Figure 8 · p. 30
• Figure 9 · p. 30
• Figure 10 · p. 31
• Figure 11 · p. 32
• Figure 12 · p. 33
• Figure 13 · p. 34
• Figure 14 · p. 35

Argument and organization

1. Motivation: efficient transitions for reward alignment

   Identifies a shared sampling bottleneck before introducing the replacement.

2. GLASS transitions, denoiser and velocity

   Builds the mechanism from a Gaussian sufficient statistic to a usable sampler.

3. Posterior sampling, sampling schemes and reward alignment

   Validates the proposed primitive before end-task gains.

Problem, claim and contribution

The contribution targets transitions used inside alignment algorithms, not another reward objective. This positioning explains compatibility with SMC, search and guidance before introducing the sufficient-statistic derivation.

§3, p.3; §4.3, p.7 · Main paper

Argument and section order

The exposition first defines a transition family, then the denoiser transformation and velocity theorem. Important limiting cases and stability details are signposted where readers would otherwise wonder whether the construction is implementable.

§4.1–4.2, pp.4–7; Appendix B.2–B.4, pp.21–23 · Main paper

Figures, captions and visual explanation

Figure 1 juxtaposes the inner-time sampling mechanism and text-image examples. Algorithm 1 then gives the precise implementation interface, preventing the intuitive inner-flow metaphor from replacing the actual computation.

Figure 1, p.2; Algorithm 1, p.4 · Main paper

Tables, comparisons and evidence

Experiments test posterior recovery and value estimation before standalone sampling and Feynman–Kac steering. Table 1 labels eight particles and 400 evaluations, distinguishing these runs from the 50-evaluation plain baseline.

§6, pp.8–10; Table 1, p.10 · Main paper

Appendix and reproducibility

The supplement includes correlation schedules, diversity, alternative parameterizations and high-guidance artifacts. It explains that even correlation one need not make the marginal transition deterministic because uncertainty about the clean sample remains.

Appendix B.5, pp.23–24; D.2–D.4, pp.28–30 · Main paper

Clarity and writing conventions

No retraining and near-negligible algebraic overhead are narrower claims than zero-cost alignment. Also, Table 2 changes image resolution for gradient guidance, so its scores should not be spliced into Table 1's controlled comparison.

§4.2, pp.6–7; Tables 1–2, p.10 · Main paper

What to reuse—and what not to infer

Transferable lesson: Validate a reusable computational primitive separately from its downstream combination, and label compute and resolution wherever comparisons change.

Boundary: Exact marginal preservation assumes perfect models and no integration error. Learned rewards can be hacked, and strong guidance produces artifacts. Appendix D.4 conflicts internally about the guidance interval and with the main text about 672 versus 676 pixels; Appendix B.6's variance-exploding inverse formula also needs verification before implementation.

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

pp.1–10, §§1–7; references pp.11–14

Appendix / supplement

pp.15–35, appendices A–D including proofs, parameterizations, stability, reward-guidance details and image grids

Visually inspected PDF pages

2, 10

• official ICLR 2026 proceedings PDF · 35 pages