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arxiv: 2604.09921 · v1 · submitted 2026-04-10 · 💻 cs.LG

A Tale of Two Temperatures: Simple, Efficient, and Diverse Sampling from Diffusion Language Models

Theo X. Olausson , Metod Jazbec , Xi Wang , Armando Solar-Lezama , Christian A. Naesseth , Stephan Mandt , Eric Nalisnick This is my paper

Pith reviewed 2026-05-10 17:03 UTC · model grok-4.3

classification 💻 cs.LG
keywords diffusion language modelssampling diversityremasking heuristicstempered samplingfork tokenspass@k evaluationautoregressive comparison
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The pith

Tempered versions of confidence-based remasking heuristics increase sample diversity in diffusion language models while retaining their speed advantages.

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

Diffusion language models generate text by iteratively denoising, but standard confidence-based remasking heuristics often produce repetitive samples because they aggressively mask low-confidence tokens. The paper introduces softened, temperature-controlled versions of these heuristics and motivates them with a formal model of fork tokens where remasking decisions affect expected entropy. This change closes the diversity gap with slower autoregressive sampling, measured by pass@k, without raising the number of function evaluations needed. The resulting samples also improve outcomes in post-training and test-time scaling experiments.

Core claim

Using an idealized model of fork tokens, the authors show that raising the temperature of confidence-based remasking increases the expected entropy at branching points during diffusion sampling; the resulting tempered heuristics produce more diverse outputs than untempered confidence remasking and match or exceed autoregressive diversity at equal computational cost.

What carries the argument

Tempered confidence-based remasking heuristics, which apply a temperature parameter to soften token selection during the reverse diffusion process.

If this is right

  • The tempered heuristics close the exploration gap (pass@k) between existing confidence-based and autoregressive sampling.
  • They outperform both methods when computational cost is held fixed (pass@NFE).
  • Higher diversity from these heuristics improves performance in downstream post-training and test-time compute scaling.
  • Simple implementation preserves the computational benefits of confidence-based methods.

Where Pith is reading between the lines

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

  • Similar temperature softening could be tested on non-diffusion generative models that use iterative masking.
  • The approach may reduce mode collapse in tasks that benefit from multiple distinct solutions, such as code generation or planning.
  • Optimal temperature values might be scheduled dynamically across denoising steps rather than held constant.

Load-bearing premise

The idealized formal model of fork tokens and their entropy under remasking accurately reflects the behavior of real diffusion language models during sampling.

What would settle it

A controlled comparison where pass@k scores with tempered heuristics remain no higher than with standard confidence-based remasking at the same number of function evaluations.

Figures

Figures reproduced from arXiv: 2604.09921 by Armando Solar-Lezama, Christian A. Naesseth, Eric Nalisnick, Metod Jazbec, Stephan Mandt, Theo X. Olausson, Xi Wang.

Figure 1
Figure 1. Figure 1: An example illustrating our model of entropy degradation. The [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pass@k for TLC (Tpos = 1) on LLaDA-8B-Instruct and Dream-7B-Instruct across four benchmarks. TLC closely tracks the AR baseline, recovering almost all of the diversity lost by low-confidence remasking. 4.1 Tempered heuristics recover pass@k scaling We start by investigating the core hypothesis that tempering the heuristics can recover pass@k scaling compared to autoregressive sampling proposed in Ni et al.… view at source ↗
Figure 3
Figure 3. Figure 3: Pass@k (top) and pass@NFE (bottom) for TCT on LLaDA-8B-Instruct. Both rows plot the same data; only the metric changes (pass@k vs pass@NFE). TCT slightly underperforms AR in pass@k, but substantially outperforms it when the cost of each sample is taken into account. TCT also outperforms deterministic confidence-thresholding (Fast￾dLLM; Wu et al. 2025) thanks to its additional source of randomness via Tpos.… view at source ↗
Figure 4
Figure 4. Figure 4: Test-time scaling for LLaDA-8B-Instruct in terms of Best@NFE when using either [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: GRPO post-training results for LLaDA-8B-Instruct on GSM8k (top) and MATH [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: TLC Tpos ablation on HumanEval with LLaDA-8B-Instruct with Ttoken = 0.8. Too little tempering (Tpos = 0.1 ) remains close to low-confidence remasking, while too much (Tpos = 2) approaches random remasking and degrades quality. Intermediate values (Tpos ∈ {0.5, 1}) strike the best balance, matching or exceeding the autoregressive baseline at high k. 1 2 4 8 16 32 64 k 0 20 40 60 80 Pass@k (%) Ttoken = 0.3 A… view at source ↗
Figure 7
Figure 7. Figure 7: Varying [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Pass@k (top) and pass@NFE (bottom) for TCT on Dream-7B-Instruct. Note that both rows plot the same data, we just vary the x-axis measure (k vs NFEs). While TCT slightly underperforms AR in pass@k, it outperforms AR when the cost of each rollout is taken into account. 1 2 4 8 16 32 64 96 k 65 70 75 80 85 90 Best@k (%) GSM8K 1 2 4 8 16 32 64 96 k 25 30 35 40 MATH 1 2 4 8 16 32 64 96 k 65 70 75 80 85 90 Best@… view at source ↗
Figure 9
Figure 9. Figure 9: Test-time scaling for LLaDA-8B-Instruct in terms of Best@ [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Mean empirical entropy of the per-question answer distributions (see Figure [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Per-question answer distributions over k = 64 samples for three GSM8K ques￾tions, comparing autoregressive, Fast-dLLM, and TCT sampling. Correct answers are marked with an asterisk (*). We observe that TCT sometimes spreads mass across a wider set of candidates (left). This illustrates the higher-entropy behavior observed in [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
read the original abstract

Much work has been done on designing fast and accurate sampling for diffusion language models (dLLMs). However, these efforts have largely focused on the tradeoff between speed and quality of individual samples; how to additionally ensure diversity across samples remains less well understood. In this work, we show that diversity can be increased by using softened, tempered versions of familiar confidence-based remasking heuristics, retaining their computational benefits and offering simple implementations. We motivate this approach by introducing an idealized formal model of fork tokens and studying the impact of remasking on the expected entropy at the forks. Empirically, the proposed tempered heuristics close the exploration gap (pass@k) between existing confidence-based and autoregressive sampling, hence outperforming both when controlling for cost (pass@NFE). We further study how the increase in diversity translates to downstream post-training and test-time compute scaling. Overall, our findings demonstrate that simple, efficient, and diverse sampling from dLLMs is possible.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes using softened, tempered versions of existing confidence-based remasking heuristics for sampling from diffusion language models (dLLMs). This approach aims to increase diversity across generated samples while retaining the computational efficiency of confidence-based methods. The authors motivate the heuristics via an idealized formal model of 'fork tokens' and the effect of remasking on expected entropy at those tokens. Empirically, the tempered heuristics are shown to close the pass@k gap to autoregressive sampling when controlling for cost via pass@NFE, and the work examines downstream effects on post-training and test-time scaling.

Significance. If the empirical results are robust and the idealized model provides a valid motivation, the contribution would be significant: it offers a simple, low-overhead way to improve exploration in dLLMs without sacrificing their speed advantage over autoregressive models. The use of pass@NFE as a cost-controlled metric is a strength, as is the analysis of scaling implications. The work addresses an under-studied aspect (diversity) in dLLM sampling literature.

major comments (2)
  1. [§3] §3 (idealized fork-token model): The central motivation rests on the claim that tempered remasking increases entropy at fork tokens in a manner that predicts improved exploration in real dLLMs. However, the model assumes independent mask decisions and Markovian dynamics; without direct empirical validation (e.g., measuring correlation of remasking events or non-Markovian dependencies in actual diffusion trajectories), the tempered heuristic's gains may be coincidental rather than mechanistically explained by the model, weakening the link between theory and the pass@k improvements.
  2. [Experimental results] Experimental results (pass@k and pass@NFE tables/figures): The reported gains lack error bars, detailed ablations on the temperature parameter, and a full experimental protocol (e.g., number of runs, seed reporting, exact hyperparameter ranges). This makes it difficult to assess whether the closure of the exploration gap is statistically reliable or generalizes beyond the tested settings, directly affecting the soundness of the main empirical claim.
minor comments (2)
  1. [§3] Notation for the temperature parameter and its relation to the two temperatures in the title could be clarified to avoid confusion with standard softmax temperature.
  2. [Figures] Some figures showing diversity metrics would benefit from additional baselines or zoomed insets for clarity at low NFE values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (idealized fork-token model): The central motivation rests on the claim that tempered remasking increases entropy at fork tokens in a manner that predicts improved exploration in real dLLMs. However, the model assumes independent mask decisions and Markovian dynamics; without direct empirical validation (e.g., measuring correlation of remasking events or non-Markovian dependencies in actual diffusion trajectories), the tempered heuristic's gains may be coincidental rather than mechanistically explained by the model, weakening the link between theory and the pass@k improvements.

    Authors: We agree that the idealized model in §3 relies on simplifying assumptions of independent mask decisions and Markovian dynamics to obtain closed-form insights on entropy at fork tokens. These assumptions enable the analytical motivation but do not capture all dependencies present in real diffusion trajectories. To address the concern, we will add empirical validation in the revised manuscript: specifically, measurements of remasking event correlations and entropy changes along actual dLLM sampling paths, comparing them against the model's predictions. We note, however, that the pass@k gains are demonstrated directly through controlled experiments and do not depend on the model for their validity; the model serves as intuition for why tempered remasking can increase diversity. revision: partial

  2. Referee: [Experimental results] Experimental results (pass@k and pass@NFE tables/figures): The reported gains lack error bars, detailed ablations on the temperature parameter, and a full experimental protocol (e.g., number of runs, seed reporting, exact hyperparameter ranges). This makes it difficult to assess whether the closure of the exploration gap is statistically reliable or generalizes beyond the tested settings, directly affecting the soundness of the main empirical claim.

    Authors: We acknowledge that the current presentation lacks sufficient statistical detail and reproducibility information. In the revised manuscript we will add error bars to all pass@k and pass@NFE tables and figures, computed across multiple independent runs with distinct random seeds. We will also include a detailed experimental protocol in the appendix that reports the exact number of runs, seed values, and the full hyperparameter ranges explored for the temperature parameter, together with additional ablations showing sensitivity to temperature. These changes will allow readers to evaluate the reliability of the reported closure of the exploration gap. revision: yes

Circularity Check

0 steps flagged

No significant circularity; idealized model and empirical results are independent of fitted inputs or self-citation chains

full rationale

The paper introduces an idealized formal model of fork tokens to motivate tempered remasking heuristics, then validates the approach via downstream empirical metrics (pass@k, pass@NFE) on real diffusion language models. No load-bearing step reduces by the paper's own equations to a fitted parameter renamed as prediction, a self-citation chain, or a definitional tautology. The central claim remains an empirical observation about diversity gains at fixed cost rather than a restatement of the model's assumptions. This is the expected non-finding for a paper whose derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on an idealized model of fork tokens whose entropy behavior under remasking is taken as representative, plus a tunable temperature parameter that controls softening; no other free parameters or invented entities are described.

free parameters (1)
  • temperature
    Softening factor applied to confidence-based remasking decisions; its value is chosen to achieve desired diversity levels.
axioms (1)
  • domain assumption Remasking decisions in diffusion language models can be usefully approximated by an idealized model of fork tokens whose expected entropy is directly affected by the remasking rule.
    Invoked to motivate why tempered heuristics increase diversity.
invented entities (1)
  • fork tokens no independent evidence
    purpose: Positions during generation where multiple token choices create branching points that control output diversity.
    New modeling construct introduced to analyze the effect of remasking on entropy.

pith-pipeline@v0.9.0 · 5492 in / 1329 out tokens · 45858 ms · 2026-05-10T17:03:38.933067+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages · 2 internal anchors

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    Evaluating Large Language Models Trained on Code

    URLhttps://arxiv.org/abs/2107.03374. Shirui Chen, Jiantao Jiao, Lillian J. Ratliff, and Banghua Zhu. dultra: Ultra-fast diffusion language models via reinforcement learning, 2025. URL https://arxiv.org/abs/2512. 21446. Daixuan Cheng, Shaohan Huang, Xuekai Zhu, Bo Dai, Xin Zhao, Zhenliang Zhang, and Furu Wei. Reasoning with exploration: An entropy perspect...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.18653/v1/n19-1423 2025

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    DAPO: An Open-Source LLM Reinforcement Learning System at Scale

    URLhttps://arxiv.org/abs/2503.14476. Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Yang Yue, Shiji Song, and Gao Huang. Does reinforcement learning really incentivize reasoning capacity in llms beyond the base model?arXiv preprint arXiv:2504.13837, 2025. Hanyang Zhao, Dawen Liang, Wenpin Tang, David Yao, and Nathan Kallus. DiFFPO: Training diff...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  3. [3]

    and Best-of-N (Snell et al., 2025). In autoregressive models, maintaining diversity during post-training has required indirect interventions such as entropy regularization (Yu et al., 2025; Cui et al., 2025; Petrenko et al., 2026), entropy-based advantage shaping (Cheng et al., 2026), or selective regularization of low-probability exploratory tokens (Huan...

    work page 2025

  4. [4]

    H pdata (xℓ 0 |x t,Jx 0K)≤ϵ

    work page

  5. [5]

    That is, the fork token’s value and the semantic outcome are tightly coupled: knowing one constrains the other to a high degree of certainty

    H pdata (Jx0K|x t,x ℓ 0)≤δ. That is, the fork token’s value and the semantic outcome are tightly coupled: knowing one constrains the other to a high degree of certainty. Repeatedly applying the chain rule, it follows immediately that Hpdata (xℓ 0 |x t)−ϵ≤H pdata (Jx0K|x t)≤H pdata (xℓ 0 |x t) +δ. (6) This aligns with the intuition in prior work (Wang et a...

    work page 2026

  6. [6]

    2.Revealing anchors linearly degrades the fork entropy: Hqℓ θ (xℓ 0 |x t′ ) =H qℓ θ (xℓ 0 |x t)− ∑ a∈A\M t′ ηa (7) where Hqℓ θ (xℓ 0 |x t)> ∑a∈A ηa >0

    There is a persistent anchor-fork confidence gap: ca t′ >c ℓ t′ for every remaining anchor a∈ A ∩ M t′. 2.Revealing anchors linearly degrades the fork entropy: Hqℓ θ (xℓ 0 |x t′ ) =H qℓ θ (xℓ 0 |x t)− ∑ a∈A\M t′ ηa (7) where Hqℓ θ (xℓ 0 |x t)> ∑a∈A ηa >0. As mentioned in Section 3.1, this model is directly inspired by (and consistent with) the empirical f...

    work page 2026