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

cs.LGApr 10, 2026

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

Authors: Theo X. Olausson, Metod Jazbec, Xi Wang, Armando Solar-Lezama, Christian A. Naesseth, Stephan Mandt, Eric Nalisnick

Organizations: Massachusetts Institute of Technology · UvA-Bosch Delta Lab, University of Amsterdam · Johns Hopkins University · University of California, Irvine

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.

Figures & tables

Figure 1: An example illustrating our model of entropy degradation. The fork token ( Definition 1 ) has high marginal uncertainty under the dLLM, indicating that both the numpy and statistics solutions are plausible. However, the dLLM is simultaneously overly confident in its prediction at the anchor tokens in the function body, biasing low-confidence remasking towards one solution as it reveals those tokens first. Tempered remasking allows the fork to still be revealed first, increasing semantic diversity without sacrificing parallelism. Note that while both paths lead to generations that match the prompt ( ), they have subtly different semantics ( ); sampling both is important to achieve good coverage.

Figure 2: Pass@

k

for TLC (

T_{\text{pos}}=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.

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. 2026a ) thanks to its additional source of randomness via

T_{\text{pos}}

Figure 4: Test-time scaling for LLaDA-8B-Instruct in terms of Best@NFE when using either self-consistency or an ORM for final answer selection. TCT performs worse compared to AR at higher NFEs when using self-consistency; however, when using an ORM, TCT improves the Pareto frontier compared to autoregressive rollouts. See Figure 11 for Best@

k

results.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6

Figure 7

Figure 7: Number of semantically distinct and well-formed outcomes when setting a fork position from Figure 6 to each of its top 5 most likely values. Overall, a majority of the fork positions produce

\geq 2

valid and semantically distinct outcomes, indicating that they play an important role in determining the semantics of the outcome (rather than just syntax).

Figure 8: TLC

T_{\text{pos}}

ablation on HumanEval with LLaDA-8B-Instruct at

T_{\text{token}}=0.8

. Too little tempering (

T_{\text{pos}}=0.1

) remains close to low-confidence remasking, while too much (

T_{\text{pos}}=2

) approaches random remasking and degrades quality. Intermediate values (

T_{\text{pos}}\in\{0.5,1\}

) strike the best balance, matching or exceeding the autoregressive baseline at high

k

Figure 9: Varying

T_{\text{token}}

for LLaDA-8B-Instruct on HumanEval. Autoregressive generation favors low temperatures, obtaining its best pass@64 at

T_{\text{token}}=0.6

. Meanwhile, low-confidence remasking scales very poorly at low token temperatures due to its greedy position selection. TLC consistently shows strong scaling and most robustness to the exact choice of

T_{\text{token}}

, matching or exceeding the best of autoregressive and low-confidence remasking in pass@64 at all temperatures. Moreover, it exhibits stronger scaling compared to low-confidence across all considered

T_{\text{token}}

, suggesting it achieves diversity through an alternative mechanism.

Figure 10: 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.

Figure 11: Test-time scaling for LLaDA-8B-Instruct in terms of Best@

k

(top) and Best@NFE (bottom) when using either self-consistency or an ORM for final answer selection. TCT performs worse compared to AR at higher NFEs when using self-consistency; however, when using an ORM, TCT improves the Pareto frontier compared to autoregressive rollouts.

Figure 12: Mean empirical entropy of the per-question answer distributions (see Figure 13 ) as a function of the group size

k

. TCT consistently yields higher-entropy answer distributions than autoregressive and confidence thresholding, particularly on GSM8K.

Figure 13: Per-question answer distributions over

k=64

samples for three GSM8K questions, 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 Figure 12 : TCT produces more diverse answers, which benefits pass@

k

and ORM-based selection but can hurt majority voting when the correct answer no longer dominates the distribution.

Figure 14: Pass@ $k$ for TLC ( $T_{\mathrm{pos}}=1$ ) on MBPP across dLLMs with different amounts of diffusion training. LLaDA-8B was trained as a diffusion model from scratch on approximately 2.3T tokens, whereas Dream-7B, LLaDA-2-mini-16B, and SDAR-1.7B were initialized from autoregressive models and subsequently diffusion-trained on approximately 580B, fewer than 200B, and 50B tokens, respectively. The LLaDA-8B and Dream-7B panels reproduce the MBPP results from Figure 2 . TLC closely tracks autoregressive sampling on the more extensively diffusion-trained LLaDA-8B and Dream-7B models, but leaves a larger gap on LLaDA-2-mini-16B and especially SDAR-1.7B.

Figure 15: Pass@ $k$ and pass@NFE for TCT on LLaDA-2-mini ( Bie et al., 2025 ) . In addition to pass@ $k$ ( Left ) and pass@NFE ( Middle ), we here additionally report pass@wall-clock-time ( Right ) to show that our proposed TCT has a negligible overhead in terms of latency compared to Fast-dLLM.

LLaDA-8B-Instruct
		$k$
Dataset	Method	1	2	4	8	16	32	64
GSM8K	Autoregressive	75.9 $\,\pm\,$ 3.1	86.9 $\,\pm\,$ 2.7	92.7 $\,\pm\,$ 2.1	96.0 $\,\pm\,$ 1.7	97.8 $\,\pm\,$ 1.4	98.6 $\,\pm\,$ 1.2	99.0 $\,\pm\,$ 1.2
	Low Confidence ( $T_{\mathrm{pos}}=0$ )	78.8 $\,\pm\,$ 3.2	87.3 $\,\pm\,$ 2.9	91.9 $\,\pm\,$ 2.5	94.6 $\,\pm\,$ 2.1	96.3 $\,\pm\,$ 1.9	97.2 $\,\pm\,$ 1.7	98.0 $\,\pm\,$ 1.5
	Random ( $T_{\mathrm{pos}}=\infty$ )	55.5 $\,\pm\,$ 2.9	73.8 $\,\pm\,$ 3.1	85.9 $\,\pm\,$ 2.8	92.4 $\,\pm\,$ 2.2	95.9 $\,\pm\,$ 1.7	97.9 $\,\pm\,$ 1.3	99.3 $\,\pm\,$ 0.8
	TLC ( $T_{\mathrm{pos}}=1$ )	72.7 $\,\pm\,$ 3.0	85.7 $\,\pm\,$ 2.7	92.3 $\,\pm\,$ 2.2	95.8 $\,\pm\,$ 1.8	97.5 $\,\pm\,$ 1.5	98.4 $\,\pm\,$ 1.2	99.0 $\,\pm\,$ 1.2

Appendix

Table 1: Pass@

k

(%) with bootstrapped 95% confidence intervals (10,000 resamples over questions/tasks, 64 samples per question,

T_{\mathrm{token}}=0.8

). Values are mean

\pm

half-width of the 95% CI. Best value per column within each dataset block in bold. Evaluation sets: GSM8K 300 questions, MATH 500, HumanEval 164 tasks, MBPP 500.

			$k$
Dataset	Method	NFE	1	2	4	8	16	32	64	96
GSM8K	Autoregressive	228	75.8 $\,\pm\,$ 3.1	86.7 $\,\pm\,$ 2.7	92.6 $\,\pm\,$ 2.1	96.0 $\,\pm\,$ 1.6	97.8 $\,\pm\,$ 1.3	98.8 $\,\pm\,$ 1.0	–	–
	Fast-dLLM	46	73.9 $\,\pm\,$ 3.1	85.5 $\,\pm\,$ 2.9	91.2 $\,\pm\,$ 2.5	94.1 $\,\pm\,$ 2.2	96.0 $\,\pm\,$ 1.9	97.1 $\,\pm\,$ 1.7	97.5 $\,\pm\,$ 1.7	97.7 $\,\pm\,$ 1.7
	TCT ( $T_{\mathrm{pos}}=0.1$ )	44	65.7 $\,\pm\,$ 2.9	81.7 $\,\pm\,$ 2.9	90.2 $\,\pm\,$ 2.4	94.5 $\,\pm\,$ 2.0	96.7 $\,\pm\,$ 1.7	97.8 $\,\pm\,$ 1.5	98.2 $\,\pm\,$ 1.5	98.3 $\,\pm\,$ 1.5
MATH	Autoregressive	243	29.6 $\,\pm\,$ 3.0	39.2 $\,\pm\,$ 3.4	48.1 $\,\pm\,$ 3.6	56.3 $\,\pm\,$ 3.7	64.0 $\,\pm\,$ 3.6	70.8 $\,\pm\,$ 3.5	–	–
	Fast-dLLM	61	30.3 $\,\pm\,$ 3.1	39.0 $\,\pm\,$ 3.6	46.4 $\,\pm\,$ 3.8	53.4 $\,\pm\,$ 3.8	60.1 $\,\pm\,$ 3.8	66.0 $\,\pm\,$ 3.8	70.6 $\,\pm\,$ 3.9	72.6 $\,\pm\,$ 3.9

Appendix

Table 2: Pass@

k

(%) for LLaDA-8B-Instruct with bootstrapped 95% confidence intervals (10,000 resamples over questions/tasks,

T_{\mathrm{token}}=0.8

\lambda=0.6

). Values are mean

\pm

half-width of the 95% CI. Evaluation sets: GSM8K 300 questions, MATH 500, HumanEval 164 tasks, MBPP 500. NFE is the average number of function evaluations per sample; for Autoregressive it is the effective generation length (tokens up to EOS), matching the pass@NFE axis of the figures.

			$k$
Dataset	Method	NFE	1	2	4	8	16	32	64	96
GSM8K	Autoregressive	200	64.6 $\,\pm\,$ 3.3	79.1 $\,\pm\,$ 2.8	89.4 $\,\pm\,$ 2.2	95.2 $\,\pm\,$ 1.6	97.8 $\,\pm\,$ 1.1	99.0 $\,\pm\,$ 0.8	–	–
	Fast-dLLM	55	69.0 $\,\pm\,$ 3.0	83.3 $\,\pm\,$ 2.8	90.9 $\,\pm\,$ 2.4	94.5 $\,\pm\,$ 2.1	96.3 $\,\pm\,$ 1.8	97.3 $\,\pm\,$ 1.7	97.8 $\,\pm\,$ 1.6	98.0 $\,\pm\,$ 1.5
	TCT ( $T_{\mathrm{pos}}=0.1$ )	51	58.2 $\,\pm\,$ 2.7	77.1 $\,\pm\,$ 2.7	89.2 $\,\pm\,$ 2.2	95.0 $\,\pm\,$ 1.7	97.6 $\,\pm\,$ 1.3	98.6 $\,\pm\,$ 1.1	99.1 $\,\pm\,$ 1.0	99.3 $\,\pm\,$ 0.8
MATH	Autoregressive	223	34.3 $\,\pm\,$ 2.9	45.9 $\,\pm\,$ 3.4	56.0 $\,\pm\,$ 3.6	64.7 $\,\pm\,$ 3.6	71.8 $\,\pm\,$ 3.5	77.3 $\,\pm\,$ 3.4	–	–
	Fast-dLLM	66	36.4 $\,\pm\,$ 3.1	47.6 $\,\pm\,$ 3.5	57.2 $\,\pm\,$ 3.6	65.3 $\,\pm\,$ 3.6	71.9 $\,\pm\,$ 3.5	77.1 $\,\pm\,$ 3.4	80.7 $\,\pm\,$ 3.3	82.2 $\,\pm\,$ 3.3

Appendix

Table 3: Pass@

k

(%) for Dream-v0-Instruct-7B with bootstrapped 95% confidence intervals (10,000 resamples over questions/tasks,

T_{\mathrm{token}}=0.8

\lambda=0.6

). Values are mean

\pm

half-width of the 95% CI. Fast-dLLM and TCT use 96 samples per question; Autoregressive uses 64–128 (dataset-dependent) and is reported to

k\leq 32

. Evaluation sets: GSM8K 300 questions, MATH 500, HumanEval 164 tasks, MBPP 500. NFE is the average number of function evaluations per sample; for Autoregressive it is the effective generation length (tokens up to EOS), matching the pass@NFE axis of the figures.

Diffusion Language Models

Diffusion language models generate and refine text through iterative denoising, enabling bidirectional context and parallel token updates.

See all 443 papers

Fork-dLLM: Avoiding the Flexibility Trap in Diffusion Language Models
Sep 30, 2026Stipe Frković, Metod Jazbec, Christian A. NaessethMasked Diffusion Models Speculative Decoding for Diffusion Language Models
University of Amsterdam · UvA-Bosch Delta Lab, University of Amsterdam
Locally Confident, Globally Stuck: The Quality-Exploration Dilemma in Diffusion Language Models
Apr 1, 2026Liancheng Fang, Aiwei Liu, Henry Peng Zou +7Diffusion Language Model Decoding Diffusion Sampling
University of Illinois Chicago · Tsinghua University · MBZUAI +1
Free Lunch for Pass@ $k$ ? Low Cost Diverse Sampling for Diffusion Language Models
Mar 5, 2026Sean Lamont, Christian Walder, Paul Montague +2Diversity-Aware Sampling Output Diversity in Language Models
Australian National University · Defence Science and Technology Group · Google DeepMind +1

Sep 30, 2026J/K move · Enter open · S save

Fork-dLLM: Avoiding the Flexibility Trap in Diffusion Language Models

Stipe Frković, Metod Jazbec, Christian A. Naesseth

University of Amsterdam · UvA-Bosch Delta Lab, University of Amsterdam

Masked Diffusion Models Speculative Decoding for Diffusion Language Models Diffusion Language Model Decoding RL for Diffusion Models Diffusion Model Inference Acceleration

Open paper AskPDF arXiv

Masked diffusion language models (dLLMs) have shown strong potential for faster inference through parallel token generation when combined with confidence-based samplers. However, recent work has shown that such methods can defer unmasking high-entropy fork positions at which multiple plausible continuations exist. This results in reduced generation diversity, as shown by worse pass@k scaling, and limits gains obtainable from RL post-training. To avoid this flexibility trap, prior work advocated for autoregressive (AR) sampling. Here, we show that discarding confidence-based sampling is unnecessary and, once inference cost is taken into account, wasteful. We first propose Fork-dLLM, a simple hybrid sampler that uses AR-style ordering only at uncertain fallback steps while retaining parallel generation otherwise. We then extend the same principle to post-training with ForkGRPO, which uses Fork-dLLM rollouts and applies the GRPO objective only at fallback steps, preserving exact policy-likelihood ratios while substantially reducing rollout and optimization cost. In our experiments, Fork-dLLM matches the strong pass@k scaling of AR sampling while being 2-3x more efficient, and ForkGRPO achieves downstream performance comparable to or better than AR-based GRPO baselines at a substantially lower training cost.

Abstract

Diffusion Language Models

Explore similar work

Fork-dLLM: Avoiding the Flexibility Trap in Diffusion Language Models

Locally Confident, Globally Stuck: The Quality-Exploration Dilemma in Diffusion Language Models

Free Lunch for Pass@kkk? Low Cost Diverse Sampling for Diffusion Language Models

Free Lunch for Pass@ $k$ ? Low Cost Diverse Sampling for Diffusion Language Models