Pith. sign in

REVIEW 4 major objections 5 minor 37 references

Diffusion language models decide which masked tokens to reveal using a local confidence score; this paper argues that for mathematics this score misleads, and it shows a training-free selection-and-mutation decoding scheme that improves LLa

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-05 00:30 UTC pith:KB5AWN5Q

load-bearing objection Useful decoding intervention for dLLM math reasoning, but the headline gain is confounded by extra compute; needs a compute-matched baseline and error bars before I'd believe the mechanism does the work. the 4 major comments →

arxiv 2608.00605 v1 pith:KB5AWN5Q submitted 2026-08-01 cs.AI

Escaping Confidence Trap: Evolutionary Decoding for Mathematical Reasoning in Diffusion LLMs

Zhenhong Sun , Hanqing Zhao , Yatao Bian , Rongcheng Tu , Liuyue Xie , Xu Zhang , Jue Wang , Davide Modolo
show 2 more authors
Daoyi Dong Dacheng Tao
This is my paper
classification cs.AI
keywords diffusion language modelsmathematical reasoningtest-time scalingconfidence-based decodingevolutionary decodingblock-wise unmaskingLLaDAdecoding trajectories
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Diffusion large language models generate text block by block, unmasking whichever tokens reach a confidence threshold. This paper asks whether that confidence-driven procedure can support mathematical reasoning, where a few digits and operators decide correctness, and answers no — it identifies a 'diffusion confidence trap' in which local confidence ratings diverge from global correctness: useful but uncertain digits get suppressed, while repetitive, confident, wrong continuations get locked in. Eight sampling runs per problem reveal two failure regimes, and pass@8 stalls around 70% on AIME, showing that simply sampling more does not escape the trap. The proposed fix, Evolutionary Decoding, treats decoding as evolution over candidate reasoning states and applies two training-free operations: step-wise selection, which boosts numerical-symbolic tokens and penalizes repetition, and block-wise mutation, which injects structured digit/symbol alternatives before a block collapses. Across six benchmarks it improves LLaDA 2.0's pass@1 over confidence-based decoding on AIME 2024/2025/2026, AMC 2023, and MATH500, and raises the pass@8 ceiling under stochastic sampling — evidence for the paper's core thesis that reliable math reasoning in diffusion LLMs requires steering the trajectory, not just increasing samples.

Core claim

Diffusion LLMs reveal masked tokens by local confidence; the paper claims this score misaligns with global math correctness — a 'diffusion confidence trap' in two regimes: sampling-sensitive failures (correct paths lost at prose-to-symbol transitions) and sampling-consistent failures (all runs reach one high-confidence wrong continuation). Pass@8 caps near 70% on AIME, so repeated sampling cannot escape it. The training-free Evolutionary Decoding intervenes in the trajectory: step-wise selection boosts uncertain digit/symbol tokens and penalizes block repetition; block-wise mutation biases logits toward digits and symbols in unsupported blocks, keeping the most confident branch. Reported res

What carries the argument

Two modifications to the block-diffusion loop of LLaDA 2.0. Step-wise selection replaces the confidence-only release rule with a score s = c + α·η·H − β·r: confidence c, plus an entropy-weighted boost (α·η·H) applied only when the top token is numerical-symbolic (η=1), minus a block repetition penalty (β·r); a fallback reveals top-K high-confidence positions if the penalty would stall the block. Block-wise mutation biases logits toward numerical and symbolic vocabulary subsets, spawning neutral, numerical, symbolic, and mixed branches when the neutral branch's confidence falls below a mutation threshold, then keeps the branch with the highest average pre-mutation confidence. The 'numerical-s

Load-bearing premise

The mechanism's selection and mutation only recognise tokens that are digits or members of a short fixed symbol list; if correctness hinges on alphabetic variables, inequalities, powers, percentages, or other operators, the method cannot tell which positions matter, so its gains should shrink or vanish on such problems.

What would settle it

Take a benchmark whose solutions rely on alphabetic variables and inequalities (a symbolic algebra set), keep the paper's exact digit/symbol regex, and compare ED against the confidence baseline: if the accuracy gain shrinks to near zero or reverses there while staying positive on a matched numeric-only set, the regex scoping is what carries the result. A second check: on AIME problems, record which of the four mutation branches wins survival selection and whether that branch actually yields a higher final-answer correctness rate than the neutral branch; if the survival rule's choice correlate

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

If this is right

  • On LLaDA 2.0-Flash, ED lifts pass@1 from 56.7 to 70.0 on AIME 2025 and from 90.0 to 95.0 on AMC 2023; on LLaDA 2.0-Mini it lifts AIME 2025 from 30.0 to 43.3, with consistent gains on AIME 2024/2026 and MATH500 as well.
  • Under eight stochastic attempts, ED improves both pass@1 and pass@8 relative to the baseline, meaning the benefit is not confined to one deterministic trajectory but improves the candidate pool itself.
  • The gains come at roughly two-to-three times the decoding steps on hard sets; the additional compute pays off on long competition-style problems, while on GSM8K's short four-to-five-block trajectories the standard mutation budget hurts and must be cut to m_max≤4 to restore a small gain.
  • A gated variant that triggers mutation only when the selection trajectory looks likely to fail (late blocks, low confidence, high repetition) raises solved AIME 2025 problems from 20/30 to 22/30 while cutting the average block index to 50.6.
  • Because the method is training-free, it can sit on top of downstream selection strategies such as majority voting or best-of-N confidence selection, whose oracle ceiling (pass@8) ED also raises.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Extension: the gains shown likely concentrate on numerically driven solutions, since the regex recognises only digits and a fixed symbol set; on problems dominated by alphabetic variables, inequalities, powers, or percents, selection and mutation would intervene at the wrong positions, and a token-aware classifier would be needed for those domains.
  • Extension: the two-regime diagnosis suggests a cheap online diagnostic — tracking block repetition ratio and digit/symbol density during decoding to predict when a trajectory needs mutation; the gated trigger is a first version of this and could be tuned per task.
  • Extension: if the confidence trap is a general property of block-wise masked decoding, analogous selection and mutation rules should transfer to other diffusion LLM families and to other precision domains such as code or formal reasoning, where the informative-token class would differ.
  • Extension: ED's step cost grows with trajectory length, so a compute-aware variant that stops mutating once a branch exits the low-support zone could keep most of the accuracy benefit at a fraction of the step budget.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies mathematical reasoning failures in the diffusion LLM LLaDA 2.0 and attributes them to a "diffusion confidence trap" in which local token confidence is misaligned with global reasoning correctness. It identifies two failure regimes, sampling-sensitive and sampling-consistent, and proposes a training-free test-time decoding framework, Evolutionary Decoding (ED). ED combines step-wise selection, which boosts the release score of numerical/symbolic tokens and penalizes repetitive blocks, with block-wise mutation, which runs four logit-bias branches and keeps the highest-confidence candidate. Experiments on AIME 2024/2025/2026, AMC 2023, MATH500, and GSM8K report accuracy gains for LLaDA2.0-Flash and LLaDA2.0-Mini over confidence-based decoding, with per-question trajectory analyses and component ablations.

Significance. If the effect is real, ED is a simple, training-free intervention for improving mathematical reasoning in diffusion LLMs and is compatible with existing test-time scaling strategies. The paper makes a useful conceptual contribution by moving from output-level repeated sampling to trajectory-level selection and mutation, and it provides unusually detailed per-question trajectory diagnostics. The calibration of alpha and beta in Appendix D is a genuine attempt to ground hyperparameters in the release-threshold boundary rather than pure grid search. The main limitation is that the empirical evidence for the central causal claim is currently confounded with additional compute: ED consistently uses substantially more decoding steps and up to four mutation branches, and no compute-matched baseline is reported. The manuscript is therefore promising but needs targeted experiments to distinguish the proposed mechanism from a best-of-N / more-compute effect.

major comments (4)
  1. [§4.1, §4.2, Tables 1, 4, 5] AIME25 is not held out. The text says all hyperparameters are selected on Flash-AIME 2025 (Tables 4 and 5) and then kept fixed, but Table 1 reports AIME25 as a main result for the same configuration. The AIME25 gains (+13.3 pts for both models) are therefore development-set results, not independent evidence. This does not invalidate the other held-out benchmarks, but the claim of "consistent gains on most competition-style benchmarks" should be re-stated with AIME25 labeled as the tuning set or removed from the headline table.
  2. [§4.2, Table 1, Figure 4, Appendix B/G] The central claim is underdetermined by a compute confound. ED uses far more decoding steps than the confidence baseline: e.g., Flash AIME24 960 vs 670, AIME25 1085 vs 669, AIME26 1113 vs 686, AMC23 878 vs 320, MATH500 310 vs 154 (Table 1). Appendix G states the overall decoding time is 2–3× higher. Figure 4 plots the steps–accuracy trade-off but draws no iso-compute line. Because the mutation stage (Eq. (6)) runs up to four parallel branches and survival selection (Eq. (8)) keeps the highest-confidence one, ED is partly a best-of-4 test-time scaling method. Without a compute-matched baseline—e.g., confidence-based decoding with the same step budget, or repeated independent samples/temperature draws with the same total forward passes—the gains cannot be attributed specifically to step-wise selection and structured mutation. This is the most important issue.
  3. [§4.3, Tables 4/5, Eqs. (6)–(8)] The ablations do not isolate the value of structured mutation from the effect of branch exploration. Table 5 varies δ, τ_mut, and m_max but always retains the four-branch structure with survival selection. There is no control with four identical neutral branches or with random logit perturbations at the same compute budget. Given Eq. (8) selects the branch with the highest average confidence, part of the observed improvement on AIME/AMC could be a generic best-of-N effect rather than the specific numerical/symbolic mutation directions. Adding such a control is necessary to support the claimed mechanism.
  4. [Table 1, Section 4.2] No error bars, confidence intervals, or significance tests are reported for any accuracy number. The AIME sets have only 30 problems: several headline differences are 3.3 pts, i.e., one problem, and one result (Mini AIME26) is exactly 0.0. With n=30, these differences are within binomial sampling noise. I recommend reporting variance over multiple decoding seeds or bootstrap intervals, and applying a simple paired test for the small AIME/AMC sets. This is particularly important because the claim of consistency across benchmarks is central to the paper.
minor comments (5)
  1. [Appendix F title] The appendix heading reads "AMIE-2025"; this should be "AIME-2025".
  2. [Eq. (8), §3.3] The phrase "prior to mutation" in the definition of \bar{c}_m^{(q)} is ambiguous: Eq. (7) defines c_m^{(t,q)} on the mutated logits, so "prior to mutation" seems to contradict the equation. Please clarify whether the selection score is computed on neutral or post-mutation confidence.
  3. [Appendix D] The calibration of α and β depends on hand-set targets c_tar and r_tar. The text says the hyperparameters are "determined from the score formulations," but these targets are user choices. Please state explicitly which values of c_tar and r_tar are used and how sensitive the final α/β are to them.
  4. [Appendix A.3] The numerical/symbolic token detector is limited to digits and a small symbol set; the paper acknowledges this in the appendix. This limitation should also be stated in Section 3 or 5, since the method's motivation is general mathematical reasoning but variables, inequalities, and powers are not covered.
  5. [Figures 8/9] Several trajectory figures show answer-extraction mismatches, e.g., Q5 pred=360 gt=336^\circ. It would help to note whether these are formatting artifacts of the extraction rule or genuine model errors.

Circularity Check

0 steps flagged

No significant circularity: ED's gains are measured on external benchmarks, hyperparameters are transferred from one tuning split, and no prediction reduces to the method's own fitted inputs.

full rationale

The paper's central claim is that Evolutionary Decoding improves LLaDA 2.0 accuracy on mathematical reasoning benchmarks. This claim is supported by pass@1 accuracy measured on AIME24/25/26, AMC23, MATH500, and GSM8K (Table 1), i.e., external benchmark outcomes rather than quantities derived from the method's equations. The selection and mutation hyperparameters (alpha, beta, delta, tau_mut, m_max) are fixed after ablations on Flash-AIME25 and then transferred unchanged to other datasets and model variants, so results outside the tuning split are genuine transfer predictions; the AIME25 tuning number is reported as a benchmark result, not as an independent prediction. Appendix D calibrates alpha and beta from hand-set targets c_tar and r_tar and the release threshold tau, not from benchmark accuracies, so there is no fitted-input-called-prediction loop. No load-bearing self-citation or imported uniqueness theorem is used; the motivation is supported by the paper's own trajectory analysis (Figure 1) and external references. The survival rule (Eq. 8) does select among mutated branches by average model confidence, which is in tension with the 'confidence trap' diagnosis, but this is a design inconsistency rather than a circular reduction: the reported gains are measured, not entailed by that choice. The absence of a compute-matched baseline (ED uses roughly 1.5-2x more decoding steps) is a serious validity or correctness concern, but it is an experimental confound, not a circularity. Consequently no circular step meets the evidence bar.

Axiom & Free-Parameter Ledger

7 free parameters · 3 axioms · 0 invented entities

The method's central claim rests on domain assumptions about which tokens matter for math reasoning, plus six hyperparameters selected on the same AIME 2025 split used in the main results. No new physical or symbolic entities are introduced.

free parameters (7)
  • alpha (selection enhancement strength) = 0.05
    Chosen from the calibration interval [alpha_loose, alpha_strict] of Appendix D, then selected by ablation on Flash-AIME 2025 (Table 4).
  • beta (repetition penalty strength) = 0.2
    Calibrated using r_tar=0.5 in Appendix D, then selected by ablation on Flash-AIME 2025 (Table 4).
  • delta (mutation logit bias) = 0.2
    Selected by ablation on Flash-AIME 2025 (Table 5).
  • tau_mut (mutation threshold) = 0.96
    Selected by ablation on Flash-AIME 2025 (Table 5).
  • m_max (maximum number of mutated blocks) = 16
    Selected by ablation on Flash-AIME 2025 (Table 5).
  • K (top-K fallback release budget) = 3
    Selected by ablation on Flash-AIME 2025 (Table 4).
  • c_tar and r_tar (calibration targets) = c_tar < 0.95, r_tar = 0.5
    Hand-chosen targets in Appendix D used to derive alpha and beta ranges; not unique.
axioms (3)
  • domain assumption Numerical and symbolic tokens are the primary determinants of mathematical reasoning correctness.
    Step-wise selection boosts tokens with eta=1 (digits/symbols) and block-wise mutation biases logits toward the same classes (Eq. 6); the entire method assumes these token classes matter most.
  • domain assumption A regex over decoded text can identify the reasoning-critical tokens.
    Appendix A.3 uses DIGIT_RE and SYMBOL_RE, and explicitly lists missing types (alphabetic variables, inequalities, powers). The method relies on this classification for both selection and mutation.
  • domain assumption Average pre-mutation confidence is a valid ranking among mutation branches.
    Eq. 8 selects the branch with maximum average released confidence, a signal the paper elsewhere says is misaligned with correctness; the survival rule assumes the ranking is reliable enough.

pith-pipeline@v1.3.0-alltime-deepseek · 27249 in / 11270 out tokens · 119495 ms · 2026-08-05T00:30:31.044727+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of Escaping Confidence Trap: Evolutionary Decoding for Mathematical Reasoning in Diffusion LLMs." pith.science (2026). https://pith.science/paper/KB5AWN5Q

@misc{pith2026260800605,
  author       = {Pith},
  title        = {Pith review of: Escaping Confidence Trap: Evolutionary Decoding for Mathematical Reasoning in Diffusion LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KB5AWN5Q}},
  note         = {Machine review of arXiv:2608.00605}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Diffusion large language models (dLLMs) have emerged as a promising alternative to autoregressive LLMs, offering efficient generation through block-wise progressive unmasking. However, their strong general-purpose performance does not necessarily translate into reliable mathematical reasoning, where correctness depends on preserving coherent numerical-symbolic reasoning trajectories. In this work, we analyze the decoding trajectories of LLaDA 2.0 and identify a recurring diffusion confidence trap: local token confidence can become misaligned with global reasoning correctness during progressive block decoding. Our analysis reveals two representative failure regimes: sampling-sensitive failures, where correct paths exist but are unstable, and sampling-consistent failures, where repeated sampling converges to repetitive high-confidence but incorrect continuations. Motivated by this observation, we propose Evolutionary Decoding, a training-free test-time scaling framework that views diffusion decoding as an evolutionary process over candidate reasoning states. The framework combines step-wise selection, which preserves useful numerical-symbolic signals and suppresses repetitive patterns, with block-wise mutation, which introduces structured alternatives to escape incorrect high-confidence basins. Experiments on multiple benchmarks show that Evolutionary Decoding improves LLaDA 2.0 over confidence-based decoding, leading to more reliable mathematical reasoning.

Figures

Figures reproduced from arXiv: 2608.00605 by Dacheng Tao, Daoyi Dong, Davide Modolo, Hanqing Zhao, Jue Wang, Liuyue Xie, Rongcheng Tu, Xu Zhang, Yatao Bian, Zhenhong Sun.

Figure 1
Figure 1. Figure 1: The diffusion confidence trap in LLaDA 2.0. (a) Eight independent runs reveal two failure regimes: sampling-consistent failures and sampling-sensitive failures. (b) Pass@8 remains bounded at 70.0%, indicating that repeated sampling alone cannot solve all failures. (c) Block￾wise statistics show distinct trajectory patterns for successful, sampling-consistent, and sampling￾sensitive cases. (d) A representat… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of Evolutionary Decoding framework for mathematical reasoning in diffusion LLMs. Given dLLM autoregressive block prediction, we intervene in the block diffusion process through step-wise selection and block-wise mutation to help escape the confidence trap. to increase the release score. This helps prevent useful but temporarily uncertain reasoning tokens from being delayed or suppressed by fluent … view at source ↗
Figure 3
Figure 3. Figure 3: Case studies on AIME-I-05 showing how Selection and Mutation further works. The full [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Steps vs. Accuracy trade-off of Baseline, Selection, and ED across six benchmarks. Each [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of Baseline and ED under 8 test-time attempts across four metrics. Red [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The relationship between the Top-1 confidence and weight for entropy enhancement of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Per-question trajectory statistics on AIME 2025. For each problem, we compare Base￾line, Selection, and Mutation in terms of the final block index, decoding steps, average confidence, and answer correctness. The mean row reports the overall block/step cost and accuracy across all 30 AIME-I/II problems. Selection reduces the average decoding steps while improving accuracy, suggesting that step-wise selectio… view at source ↗
Figure 8
Figure 8. Figure 8: Block-wise confidence and decoding-step analysis on AIME2025-I. The left axis denotes the average confidence of symbol/digit tokens, and the right axis denotes the decoding steps. Green curves indicate correct trajectories, while red curves indicate incorrect ones. Suc￾cessful trajectories are compact and stable, whereas failures mainly follow two modes: sampling￾consistent failures stay highly confident b… view at source ↗
Figure 9
Figure 9. Figure 9: Block-wise confidence and decoding-step analysis on AIME2025-II. The left axis denotes the average confidence of symbol/digit tokens, and the right axis denotes the decoding steps. Green curves indicate correct trajectories, while red curves indicate incorrect ones. Suc￾cessful trajectories are compact and stable, whereas failures mainly follow two modes: sampling￾consistent failures stay highly confident … view at source ↗
Figure 10
Figure 10. Figure 10: Block-wise confidence and decoding-step analysis of Selection on AIME2025-I. The left axis shows the average confidence of symbol/digit tokens, and the right axis shows the decoding steps. Green and red curves denote correct and incorrect trajectories, respectively. Compared with the baseline, Selection reduces the average block index from 87.9 to 57.3 and the average steps from 709.0 to 604.1, while reco… view at source ↗
Figure 11
Figure 11. Figure 11: Block-wise confidence and decoding-step analysis of Selection on AIME2025-II. Compared with the baseline, Selection preserves similar average block confidence while improving the number of solved problems to 11/15. Several previously unstable trajectories are redirected to correct answers with more compact symbolic/numerical evolution, suggesting that step-wise selec￾tion helps suppress redundant low-info… view at source ↗
Figure 12
Figure 12. Figure 12: Effect of Mutation over Selection on AIME2025-I. Yellow-shaded regions indicate blocks within the first 16 block indices where structured mutation is applied. Compared with Selec￾tion, Mutation introduces more diverse trajectory evolution in the early stage, which helps escape some incorrect but stable reasoning paths and recover additional hard cases. This also shows that early selective mutation can inc… view at source ↗
Figure 13
Figure 13. Figure 13: Effect of Mutation over Selection on AIME2025-II. Yellow-shaded regions denote the first 16 block indices where mutation is triggered. Compared with Selection, Mutation pro￾duces more diverse block-wise confidence trajectories, indicating that early structured perturbation effectively broadens the explored reasoning branches. While this added diversity does not always translate into immediate accuracy gai… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

37 extracted references · 12 canonical work pages

  1. [1]

    Large language diffusion models,

    S. Nie, F. Zhu, Z. You, X. Zhang, J. Ou, J. Hu, J. Zhou, Y . Lin, J.-R. Wen, and C. Li, “Large language diffusion models,”arXiv preprint arXiv:2502.09992, 2025

    Pith/arXiv arXiv 2025

  2. [2]

    Llada2. 0: Scaling up diffusion language models to 100b,

    T. Bie, M. Cao, K. Chen, L. Du, M. Gong, Z. Gong, Y . Gu, J. Hu, Z. Huang, Z. Lan,et al., “Llada2. 0: Scaling up diffusion language models to 100b,”arXiv preprint arXiv:2512.15745, 2025

    Pith/arXiv arXiv 2025

  3. [3]

    Dream 7b: Diffusion large language models,

    J. Ye, Z. Xie, L. Zheng, J. Gao, Z. Wu, X. Jiang, Z. Li, and L. Kong, “Dream 7b: Diffusion large language models,”arXiv preprint arXiv:2508.15487, 2025

    Pith/arXiv arXiv 2025

  4. [4]

    Diffusion of thought: Chain-of-thought reasoning in diffusion language models,

    J. Ye, S. Gong, L. Chen, L. Zheng, J. Gao, H. Shi, C. Wu, X. Jiang, Z. Li, W. Bi,et al., “Diffusion of thought: Chain-of-thought reasoning in diffusion language models,”Advances in Neural Information Processing Systems, vol. 37, pp. 105345–105374, 2024

    work page 2024

  5. [5]

    Beyond autoregression: Discrete diffusion for complex reasoning and planning,

    J. Ye, J. Gao, S. Gong, L. Zheng, X. Jiang, Z. Li, and L. Kong, “Beyond autoregression: Discrete diffusion for complex reasoning and planning,”arXiv preprint arXiv:2410.14157, 2024

    Pith/arXiv arXiv 2024

  6. [6]

    Reasoning in diffusion large language models is concen- trated in dynamic confusion zones,

    R. Chen, M. Chen, and K. Wang, “Reasoning in diffusion large language models is concen- trated in dynamic confusion zones,”arXiv preprint arXiv:2511.15208, 2025

    arXiv 2025

  7. [7]

    Llada 1.5: Variance-reduced preference optimization for large language diffusion models,

    F. Zhu, R. Wang, S. Nie, X. Zhang, C. Wu, J. Hu, J. Zhou, J. Chen, Y . Lin, J.-R. Wen,et al., “Llada 1.5: Variance-reduced preference optimization for large language diffusion models,” arXiv preprint arXiv:2505.19223, 2025

    Pith/arXiv arXiv 2025

  8. [8]

    Training verifiers to solve math word problems,

    K. Cobbe, V . Kosaraju, M. Bavarian, M. Chen, H. Jun, L. Kaiser, M. Plappert, J. Tworek, J. Hilton, R. Nakano,et al., “Training verifiers to solve math word problems,”arXiv preprint arXiv:2110.14168, 2021

    Pith/arXiv arXiv 2021

  9. [9]

    d1: Scaling reasoning in diffusion large language models via reinforcement learning,

    S. Zhao, D. Gupta, Q. Zheng, and A. Grover, “d1: Scaling reasoning in diffusion large language models via reinforcement learning,”arXiv preprint arXiv:2504.12216, 2025. 10

    Pith/arXiv arXiv 2025

  10. [10]

    Dirl: An efficient post-training framework for diffusion language models,

    Y . Zhu, J. Wan, X. Liu, S. He, Q. Wang, X. Guo, T. Liang, Z. Huang, Z. He, and X. Qiu, “Dirl: An efficient post-training framework for diffusion language models,”arXiv preprint arXiv:2512.22234, 2025

    arXiv 2025

  11. [11]

    Self-consistency improves chain of thought reasoning in language models,

    X. Wang, J. Wei, D. Schuurmans, Q. Le, E. Chi, S. Narang, A. Chowdhery, and D. Zhou, “Self-consistency improves chain of thought reasoning in language models,”arXiv preprint arXiv:2203.11171, 2022

    Pith/arXiv arXiv 2022

  12. [12]

    Scalable best-of-n selection for large language models via self-certainty,

    Z. Kang, X. Zhao, and D. Song, “Scalable best-of-n selection for large language models via self-certainty,”arXiv preprint arXiv:2502.18581, 2025

    arXiv 2025

  13. [13]

    Confidence-based decoding is provably efficient for diffusion language models,

    C. Cai and G. Li, “Confidence-based decoding is provably efficient for diffusion language models,”arXiv preprint arXiv:2603.22248, 2026

    arXiv 2026

  14. [14]

    Locally confident, globally stuck: The quality-exploration dilemma in diffusion language models,

    L. Fang, A. Liu, H. P. Zou, Y . Chen, E. Ma, L. Pan, C. Miao, W.-C. Huang, X. Liu, and P. S. Yu, “Locally confident, globally stuck: The quality-exploration dilemma in diffusion language models,”arXiv preprint arXiv:2604.00375, 2026

    arXiv 2026

  15. [15]

    Remasking discrete diffusion models with inference-time scaling (2025),

    G. Wang, Y . Schiff, S. S. Sahoo, and V . Kuleshov, “Remasking discrete diffusion models with inference-time scaling (2025),”arXiv preprint arXiv:2503.00307

    arXiv 2025

  16. [16]

    Rfg: Test-time scaling for diffusion large lan- guage model reasoning with reward-free guidance,

    T. Chen, M. Xu, J. Leskovec, and S. Ermon, “Rfg: Test-time scaling for diffusion large lan- guage model reasoning with reward-free guidance,”arXiv preprint arXiv:2509.25604, 2025

    arXiv 2025

  17. [17]

    Improving diffusion language model decoding through joint search in generation order and token space,

    Y . Shen, T. Feng, J. Han, W. Wang, T. Chen, C. Shen, J. Leskovec, and S. Ermon, “Improving diffusion language model decoding through joint search in generation order and token space,” arXiv preprint arXiv:2601.20339, 2026

    arXiv 2026

  18. [18]

    Prism: Efficient test-time scaling via hierarchical search and self-verification for discrete diffusion language models,

    J. Bai, Y . Li, Y . Zhu, Y . Xin, Q. Shi, A. Feng, X. Liu, M. Tao, J. Xue, X. Li,et al., “Prism: Efficient test-time scaling via hierarchical search and self-verification for discrete diffusion language models,”arXiv preprint arXiv:2602.01842, 2026

    Pith/arXiv arXiv 2026

  19. [19]

    S3: Stratified scaling search for test-time in diffusion language models,

    A. Bilal, M. A. Mohsin, M. Umer, A. Aali, M. U. Khanzada, M. U. Rafique, Z. He, E. Fox, and D. F. Hougen, “S3: Stratified scaling search for test-time in diffusion language models,” arXiv preprint arXiv:2604.06260, 2026

    Pith/arXiv arXiv 2026

  20. [20]

    Test-time scaling in diffusion llms via hidden semi-autoregressive experts,

    J. Lee, H. Moon, K. Zhai, A. K. Chithanar, A. K. Sahu, S. Kar, C. Lee, S. Chakraborty, and A. S. Bedi, “Test-time scaling in diffusion llms via hidden semi-autoregressive experts,”arXiv preprint arXiv:2510.05040, 2025

    arXiv 2025

  21. [21]

    Structured denoising dif- fusion models in discrete state-spaces,

    J. Austin, D. D. Johnson, J. Ho, D. Tarlow, and R. Van Den Berg, “Structured denoising dif- fusion models in discrete state-spaces,”Advances in neural information processing systems, vol. 34, pp. 17981–17993, 2021

    work page 2021

  22. [22]

    Likelihood-based diffusion language models,

    I. Gulrajani and T. B. Hashimoto, “Likelihood-based diffusion language models,”Advances in Neural Information Processing Systems, vol. 36, pp. 16693–16715, 2023

    work page 2023

  23. [23]

    Discrete diffusion modeling by estimating the ratios of the data distribution,

    A. Lou, C. Meng, and S. Ermon, “Discrete diffusion modeling by estimating the ratios of the data distribution,”arXiv preprint arXiv:2310.16834, 2023

    Pith/arXiv arXiv 2023

  24. [24]

    Simplified and generalized masked diffusion for discrete data,

    J. Shi, K. Han, Z. Wang, A. Doucet, and M. Titsias, “Simplified and generalized masked diffusion for discrete data,”Advances in neural information processing systems, vol. 37, pp. 103131–103167, 2024

    work page 2024

  25. [25]

    Simple and effective masked diffusion language models,

    S. S. Sahoo, M. Arriola, Y . Schiff, A. Gokaslan, E. Marroquin, J. T. Chiu, A. Rush, and V . Kuleshov, “Simple and effective masked diffusion language models,”Advances in Neural Information Processing Systems, vol. 37, pp. 130136–130184, 2024

    work page 2024

  26. [26]

    Scaling up masked diffusion models on text,

    S. Nie, F. Zhu, C. Du, T. Pang, Q. Liu, G. Zeng, M. Lin, and C. Li, “Scaling up masked diffusion models on text,”arXiv preprint arXiv:2410.18514, 2024

    Pith/arXiv arXiv 2024

  27. [27]

    Block diffusion: Interpolating between autoregressive and diffusion language models,

    M. Arriola, A. Gokaslan, J. T. Chiu, Z. Yang, Z. Qi, J. Han, S. S. Sahoo, and V . Kuleshov, “Block diffusion: Interpolating between autoregressive and diffusion language models,”arXiv preprint arXiv:2503.09573, 2025

    Pith/arXiv arXiv 2025

  28. [28]

    Mercury: Ultra-fast language models based on diffusion,

    S. Khanna, S. Kharbanda, S. Li, H. Varma, E. Wang, S. Birnbaum, Z. Luo, Y . Miraoui, A. Pal- recha, S. Ermon,et al., “Mercury: Ultra-fast language models based on diffusion,”arXiv e- prints, pp. arXiv–2506, 2025

    work page 2025

  29. [29]

    Llada-moe: A sparse moe diffusion language model,

    F. Zhu, Z. You, Y . Xing, Z. Huang, L. Liu, Y . Zhuang, G. Lu, K. Wang, X. Wang, L. Wei, et al., “Llada-moe: A sparse moe diffusion language model,”arXiv preprint arXiv:2509.24389, 2025. 11

    arXiv 2025

  30. [30]

    Chain- of-thought prompting elicits reasoning in large language models,

    J. Wei, X. Wang, D. Schuurmans, M. Bosma, F. Xia, E. Chi, Q. V . Le, D. Zhou,et al., “Chain- of-thought prompting elicits reasoning in large language models,”Advances in neural infor- mation processing systems, vol. 35, pp. 24824–24837, 2022

    work page 2022

  31. [31]

    Scaling llm test-time compute optimally can be more effective than scaling model parameters,

    C. Snell, J. Lee, K. Xu, and A. Kumar, “Scaling llm test-time compute optimally can be more effective than scaling model parameters,”arXiv preprint arXiv:2408.03314, 2024

    Pith/arXiv arXiv 2024

  32. [32]

    Advancing block diffusion language models for test-time scaling,

    Y . Lu, D. Kong, J. Wang, L. Guo, X. Wang, Q. Guo, T. Gui, X. Huang, W. Ye, S. Zhang, et al., “Advancing block diffusion language models for test-time scaling,”arXiv preprint arXiv:2602.09555, 2026

    work page arXiv 2026

  33. [33]

    Introduction to evolutionary computing,

    A. Eiben and J. Smith, “Introduction to evolutionary computing,” 2003

    work page 2003

  34. [34]

    Evolutionary computation: a unified approach,

    K. De Jong, “Evolutionary computation: a unified approach,” inProceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 373–388, 2017

    work page 2017

  35. [35]

    Connecting large language models with evolutionary algorithms yields powerful prompt optimizers,

    Q. Guo, R. Wang, J. Guo, B. Li, K. Song, X. Tan, G. Liu, J. Bian, and Y . Yang, “Connecting large language models with evolutionary algorithms yields powerful prompt optimizers,”arXiv preprint arXiv:2309.08532, 2023

    Pith/arXiv arXiv 2023

  36. [36]

    When large language models meet evolutionary algorithms,

    W. Chao, J. Zhao, L. Jiao, L. Li, F. Liu, and S. Yang, “When large language models meet evolutionary algorithms,”arXiv e-prints, pp. arXiv–2401, 2024

    work page 2024

  37. [37]

    Sglang: Efficient execution of structured language model programs,

    L. Zheng, L. Yin, Z. Xie, C. Sun, J. Huang, C. H. Yu, S. Cao, C. Kozyrakis, I. Stoica, J. E. Gon- zalez,et al., “Sglang: Efficient execution of structured language model programs,”Advances in neural information processing systems, vol. 37, pp. 62557–62583, 2024. 12 Table 7: Details of the mathematical reasoning benchmarks used in our evaluation. Dataset #...

    work page 2024