ParallelBench: Understanding the Trade-offs of Parallel Decoding in Diffusion LLMs
Authors: Wonjun Kang
Kevin Galim
Seunghyuk Oh
Minjae Lee
Yuchen Zeng
Shuibai Zhang
Coleman Richard Charles Hooper
Yuezhou Hu
Hyung Il Koo
Nam Ik Cho
Kangwook Lee
Venue: ICLR 2026 Poster (2026)
Keywords: diffusion LLMs
parallel decoding
benchmark
Primary area: foundation or frontier models, including LLMs

Abstract: While most autoregressive LLMs are constrained to one-by-one decoding, diffusion LLMs (dLLMs) have attracted growing interest for their potential to dramatically accelerate inference through parallel decoding. Despite this promise, the conditional independence assumption in dLLMs causes parallel decoding to ignore token dependencies, inevitably degrading generation quality when these dependencies are strong. However, existing works largely overlook these inherent challenges, and evaluations on standard benchmarks (e.g., math and coding) are not sufficient to capture the quality degradation caused by parallel decoding. To address this gap, we first provide an information-theoretic analysis of parallel decoding. We then conduct case studies on analytically tractable synthetic list operations from both data distribution and decoding strategy perspectives, offering quantitative insights that highlight the fundamental limitations of parallel decoding. Building on these insights, we propose ParallelBench, the first benchmark specifically designed for dLLMs, featuring realistic tasks that are trivial for humans and autoregressive LLMs yet exceptionally challenging for dLLMs under parallel decoding. Using ParallelBench, we systematically analyze both dLLMs and autoregressive LLMs, revealing that: (i) dLLMs under parallel decoding can suffer dramatic quality degradation in real-world scenarios, and (ii) current parallel decoding strategies struggle to adapt their degree of parallelism based on task difficulty, thus failing to achieve meaningful speedup without compromising quality. Our findings underscore the pressing need for innovative decoding methods that can overcome the current speed-quality trade-off. We release our benchmark to help accelerate the development of truly efficient dLLMs.

Published as a conference paper at ICLR 2026
PARALLELBENCH: UNDERSTANDING THE TRADE- OFFS OF PARALLEL DECODING IN DIFFUSION LLMs
Wonjun Kang" 1.5
Kevin Galim
Seunghyuk Oh"
Minjae Leel
Yuchen Zeng..
Shuibai Zhang
Coleman Hooper Kangwook 2
Yuezhou Hu*
Hyung Il Koo'
Nam Ik Cho
FuriosaAI 2 UadMaddoon
3 Microsoft Research 4 UC Berkeley KRAFTONN
5 Scoul National University
Ludo Robotics
Project Page: http:://pparallelbennc..tt ii
Leaderboard: http:: httpebbonrdttttsssppaaaaaaaaeeee hetttss//paraalleeeeecc..ghhhhh http::/htttt.....eeeeeeeoet.oooo
i leaderboard/ Bench
GitHub: httpps:://ittibbcc/////frrr/rr
ABSTRACT
While most autoregressive LLMs are constrained to one-by-one decoding, dif- fusion LLMs (dLLMs) have attracted growing interest for their potential to dra- matically accelerate inference through parallel decoding. Despite this promise, the conditional independence assumption in dI.LMs causes parallel decoding to ignore token dependencies, inevitably degrading generation quality when these dependencies are strong. However, existing works largely overlook these inher- ent challenges, and evaluations on standard benchmarks (e.g., math and coding) are not sufficient to capture the quality degradation caused by parallel decoding. To address this gap. we first provide an information thhooreti analysis of parallel decoding. We then conduct case studies analytically tractable synthetic list op- erations from both data distribution and decoding strategy perspectives, offering quantitative insights that highlight the fundamental limitations of parallel decod- ing. Building on these insights, we propose PARALLEA BARALLELBENCH, the first bench- mark specifically designed for dLLMs, featuring realistic tasks that are trivial for humans and autoregressive LLMs yet exceptionally challenging for dLLMs un- der parallel decoding. Using BARALLELBENCH,
systematically analyze both dLLMs and autoregressive LLMs, revealing that: (i) dLLMs under parallel decod- ing can suffer dramatic quality degradation in real-world scenarios, and (ii) current parallel decoding strategies struggle to adapt their degree of parallelism based on task difficulty, thus failing achieve meaningful speedup without compromis- ing quality. Our findings underscore the pressing need for innovative decoding methods that can overcome the current speed-quality trade-off. We release our benchmark to help accelerate the development of truly efficient dLLMss.
INTRODUCTION
Large Language Models (LLMs) (Brown et al., 2020; Touvron et al., 2023) have achieved remark- able success in natural language processing, including complex reasoning (Jaech et al., 2024; Guo et al., 2025) and code generation (Jiang et al., 2024), which require extensive generation lengths. However, the autoregressive nature of most current LLMs fundamentally constrains inference speed, as they must generate tokens one-by-one. Unlike autoregressive LLMs, which follow (i) one-by-one decoding and (ii) left-to-right decoding, diffusion LLMs (dLLMs) enable (i) parallel decoding and (ii) any-order decoding. Recently, there has been a rapidly growing interest in dLLMs for their potential to dramatically accelerate LLM inference via parallel decoding. While early diffusion language models suffered from performance gaps compared to autoregressive models, recent ad- vances (Inception Labs al., 2025; Song et al., 2025) have shown that dL. can achieve compa- rable generation quality to autoregressive LLMs, potentially emerging as next-generation LLMs.
"Equal Contribution. Fmails: (kangwj 1995, kevin.gal g.w.galm seunghyukoh ffrr fur osa ai.

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Published as a conference paper at ICLR 2026
Limitations of Parallel Decoding
A Case Study on List Operations
ParallelBench
Pick a candom city for travel: New York New Orteans, Mexico City, or Panama City?
Q. Bepiane a random item in A, B, C with
Consiats of tasks across catlgoriia
88% 33%
Warling Line
Text Wrrting
Puzzles
Johnt
-33
Focenccy
Assuray
Ore-ty-dre
POLPS
Acce 3x
(3 333 3)
44.4%
# Tooks
ParaBal
POWPS
(8 (P)
Covers wide-range of difficulty levels
Massuiing ttokens unmosked poralee
Gary-to-panndate Hiard-toppandltt toee
Paralellench
Prmpptx
Shuffle following items A, R,
33%
A 33%
38%
Plasiediars
Plan
A. New City
Acc+ 3 3"3
22.25
*: One by One
* Fully Pansllal
first benchmerk to assess trade-ofts of parallel decoding in dLLMs
Parallel decoding ignores token depandencies
Quality incvitably drops under paralial docoding
Figure I: BRALLELLENNH (left) Parallel decoding fails to capture token dependencies, risking incorrect combinations of individually likely tokens (e.g.. "New" and "City"). (middle) Quantita- tive analysis of parallel decoding performance on list operations. (right) Based on our findings, we develop a realistic benchmark to evaluate the speed-quality trade-off of parallel decoding methods.
However, the conditional independence assumption (Wu et al., 2025) in dLLMs causes parallel decoding to fail to capture token dependencies, resulting in significant quality degradation. As shown in Fig. 1, under parallel decoding, the model might generate " "New City" instead of the correct "New York" or "Mexico City" because each token is unmasked independently without considering its mutual constraints. Existing works on dLLMs (Nie et al., 2025; Ye et al.. 2025b) mainly explore their one-by-one decoding quality with limited analysis of parallel decoding challenges, despite parallel generation being their defining advantage. Moreover, current evaluations rely on standard benchmarks, such as math (Cobbe et al., 2021) and coding (Chen et al., 2021), which may not adequately expose the quality degradation of parallel decoding in real-world scenarios.
To address this gap, we first provide an information- thhorrttc analysis of parallel decoding in dLLMs, showing that even ideal models suffer increasing difficulty due to inherent token dependen- cies in the data distribution as the degree of parallelism increases. To further provide quantitative insights, we conduct case studies analytically tractable synthetic list operations from two perspec- tives: (i) from the data distribution perspective, we quantitatively formulate the difficulty of parallel decoding through conditional total correlation, proving that certain list operations exhibit inevitable quality degradation under parallel decoding, and (ii) from the decoding order perspective, we derive the achievable accuracy of various unmasking strategies on these tasks, showing that accuracy varies significantly across different unmasking strategies.
Building on this, propose PARALLEL BENCH demonstrate that the quality degradation from parallel decoding extends beyond synthetic to real-worid scenarios. This realistic benchmark en- compasses tasks of varying difficulty under parallel decoding, including those that are exceptionally challenging for parallel decoding in dLLMs yet still trivial for humans and autoregressive LLMs. Using this benchmark, we conduct extensive evaluations of dLLMs and autoregressive LLMss, re- vealing two key findings. First, consistent with our synthetic results, dLLMs with parallel decoding exhibit severe quality degradation, even on trivial real-world tasks. Second, current parallel decoding strategies struggle to adaptively adjust the degree of parallelism based on task difficulty, resulting in suboptimal speed-qualle trade-offs. Finally, we explore additional techniques to determine if they can improve the current trade-offss in parallel decoding. In summary, main contributions are:
We provide an information-theoree analysis to formalize the quality degradation in parallel de- coding arising from token dependencies and design tractable synthetic tasks to quantify its impact.
We introduce PARALLELBENCHI the first realistic benchmark for evaluating trade-off's of parallel decoding in dLLMs, covering diverse difficulty levels to assess adaptive parallelism strategies.
Through extensive experiments PARALLELBENCH, der parallel decoding suffer severe quality degradation on seemingly simple tasks, and existing decoding strategies struggle to adaptively balance speed and quality.
demonstrate that current dLLMs un-
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2 RELATED WORKS
Diffusion-based Language Models D3PM (Austin et al., 2021) pioneered applying diffusion models to discrete data by modeling discrete diffusion processes through various transition matrices. Diffusion-LM (Li et al., 2022) introduced a non-autoregreessiee language model using continuous diffusion. Lou et al. (2024) introduced SEDD, which parameterizes discrete diffusion processes by learning concrete scores through a novel score entropy loss, thereby achieving performance compa- rable to that of autoregressive models. Sahoo al. (2024); Shi et al. (2024) showed that masked diffusion with absorbing state achieves stronger performance through simplified framework. Re- cent diffusion-bar -based language models (Kim al., 2025c) have achieved significant improvements in scale and performance, establishing practical dLLMs (Nie et al., 2025; Zhu et al., 2025; Ye et al., 2025b; Kim et al., 2025d) with expanded multimodal capabilities (You et al., 2025; Yang et al., 2025b) and variants for complex reasoning (Zhao et al., 2025) and code generation (Gong et al., 2025; Inception Labs et al., 2025; Song et al., 2025).
Analysis of Decoding Mechanisms in dLLMSs Wu et al. (2025) discussed the quality degradation in dLLMs' parallel decoding process due to the conditional independence assumption, proposing threshold-baat -bseed and factor-based unmasking methods to mitigate this issue. However, they only focus on standard benchmarks like GSM8K (Cobbe et al., 2021) and HumanEval (Chen et al., 2021) rather than exploring settings where parallel decoding is particularly vulnerable. Feng et al. (2025) demonstrated that dLLMs' parallel decoding is highly task-dependent: efficient for fluent text gen- eration with constant steps, but ineffective for reasoning tasks requiring linearly scaling steps for leveel correctness. However, this work offers limited validation, relying highly syn- thetic settings like n-grams and Hidden Markov Models. Gong et al. (2025) introduced AR-ness metrics to quantify the similarity between dLLM and autoregressive LLM decoding orders. They found that dLLMs exhibit any-order decoding, with AR-ness varying by dataset and correlating with quality degradation in parallel decoding. However, their analysis is limited standard benchmarks, such as code and math. Ye et al. (2025a) demonstrated that dLLMs surpass autoregressive LLMs in complex reasoning and long-term planning tasks, such as Countdown and Sudoku.
For broader overview of related work, see Appendix B.
3 PRELIMINARIES: DIFFUSION LLM DECODING
Since most dLLMs (Nie et al., 2025; Ye et al., 2025b) employ masked diffusion (Sahoo et al., 2024), we assume masked diffusion throughout this paper. For more detailed discussion, see Appendix B.3.
Parallel Decoding In parallel decoding, dLLMs generate tokens over T timesteps with target se- quence Y S1 U S2 U... U Sr. At timestep t'. the model generates token set St conditioned on input X and previously generated tokens Set S1 U... U S.-1- The generation probability is factorized (o( = - Po Xx Se)., assuming conditional independence among tokens in S.. This conditional independence assumption enables parallel decoding within each timestep but introduces factorization errors from unmodeled token dependencies, creating a funda- mental speed-quality trade-off. These errors arise with strong semantic syntactic dependencies, as shown in Fig. 1: dLLMss sample from factorized marginals (X)y Po Po(y441] lX) instead of the true joint (y [X), potentially generating invalid combinations like "New City" rather than "New York" or "Mexico City". In the special case of one-step generation (T' = 1), Huang al. (2022) proved that the minimum achievable KL divergence between the factorized model Po(Y Nger PX(yilX) and the true data distribution Pana (Y is lower-bounded by the conditional total correlation C(Y)X) Haata
H (Y)x) + EnErr Hasta (M(X))
ming PKI.(Pann (Y|X) II Pa(Y 2 C(Y[X)
X quantifies the difficulty of parallel generation by measuring token dependencies, imposing fundamental limits that even optimally designed models cannot overcome.
For intuitive understanding, use notation t 0 to t T where t corresponds to the f-th parallel decoding step, rather than the typical reverse time notation in diffusion models.
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Any-order Decoding: Token Unmasking Methods dLLMs can decode in any order, where the unmasking strategy determines how to partition Y into disjoint sets S1 U ...U. Sr, critically im- pacting output quality. At each timestep, dLLMs make predictions for all masked token positions but only unmask and finalize a subset of them, keeping the rest masked for subsequent timesteps. Unmasking methods can be broadly categorized into two approaches: (i) Top-k (static): which un- masks a fixed number of tokens in left-to-right order, randomly, or based on a scoring metric (c.g., confidence (Nie et al., 2025), margin (Kim al., 2025b), and entropy (Ye et al., 2025b)), and (ii) Threshold (adaptive): which unmasks tokens whose scores exceed a certain threshold; if no to- kens meet the threshold, the single token with the highest score unmasked. Furthermore, several works (Nie et al., 2025; Arriola et al., 2025) adopt semi-autoregreesive (semi-AR) decoding, which divides sequences into fixed-size blocks decoded left-to-right, where tokens within each block are generated in parallel using any unmasking strategy once preceding blocks are complete.
4 THEORETICAL ANALYSIS OF PARALLEL DECODING
In this section, we thcoretically explore the specific quality degradation that occurs in the case of T-step parallel decoding, and then provide quantitative analyses from both data distribution and decoding strategy perspectives, using analytically tractable synthetic list operations.
Theorem 1 (Lower Bound for T Tsseep Parallel Decoding). For factorized generative model (e.g., dLLM) (x( performing T-step parallel decoding, assume the target sequence Y is partitioned into T disjoint sets, Y = Si U S2 U ... U ST. At each step E [l....,TT) the model generates the tokens in set S; in parallel, conditioned on X and all previously generated tokens Sei = S1 U S2 U S..US <5 0). The minimum achievable KL divergence for this model is lower-bounded by:
ming DEL ( || Po(Y(X)) 2 L1
(2)
where C(S,)X, Ses) denotes the conditional total correlation of tokens in St given X and Sei. The equality holds when Po(y, |X, S2z) Pasta (y, X Sei) for all E {l....,T) and for all yj E Sy, Remark 1 (Boundary Cases). The lower bound Lr captures the two boundary cases of the decoding spectrum: i) When T 1, L = X): ii When T = |Y| (i.e., one-by-one decoding with S = {wn for all i). each i we have C(S
thus fiy1 0.
Theorem 2 (Monotonicity of Error Bounds). Let L denote the optimal (minimum) error bound over all possible T-step partitions {5:) C == min (T((S.)= Then Lip is monoton- ically decreasing with respect to the number of generation steps: C7 2 CT+1-
Remark 2. Since L = XX) and Liv 0, the optimal error bound Li forms monotonically decreasing function from the total correlation CX) to zero as T increases from 1 to |Y}.
See Appendix A for proofs and Appendix A.3 for the extension of Theorem 2 to input-dependent partitions. Theorem shows that 7-step parallel decoding in dLLMMs inevitably incurs distribution error due to data distribution properties such as conditional total correlation (e.g., C(Y]X), even with ideal models. Theorem 2 further establishes that the lower bound on this distribution error increases monotonically as T' decreases. However, C(Y[X) is intractable real-world datasets, though Huang et al. (2022) approximated it with well-trained transformer.
To address this gap, we use synthetic list operations with analytically tractable C(Y]X). We examine four tasks on length-n input sequences (c.g., [A, B, C. D, E)): (i) Copy: copying the input; (i) Replace Index: replacing an item at given index with F; (iii) Replace Random: replacing one random item with F; and (iv) Shuffle: rearranging the items.
4.1 A CASE STUDY ON LIST OPERATIONS: DATA DISTRIBUTION PERSPECTIVE
Copy & Replace Index While Replace Index seems harder than Copy, both tasks are equally simple from the perspective of C(Y)X). . For both tasks, each output token ye is uniquely determined by X alone (C(Y)X)= = 0), allowing ideal models to decode in parallel without distribution error.
Replace Random While Replace Index seems harder than Replace Random (requiring replace- ment at given index), from the perspective of C(Y)X), the opposite holds. While Replace Index
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yields C(YJX) = 0, Replace Random exhibits token dependencies since replacing exactly one domly selected item requires all others to remain unchanged, yielding:
C( = (n 1)[logg(n) - logz(n 1)], lim C(Y = logg(e) RJ 1.44.
(3)
This indicates that the difficulty of parallel decoding remains bounded for arbitrarily long sequences.
Shuffle Shuffle generates a random permutation and exhibits stronger token dependencies than Replace Random, as once an item is placed at any position, it cannot appear elsewhere. This yields:
[( = n (n) - log2 (n!), lim C( = oo,
(4)
indicating that the difficulty of capturing permutation constraints grows without bound for arbi- trarily long sequences in one-step generation. For 7'step parallel decoding, CT((S.)==)
E [s.] (kg)(k)) log)(n!), where h2 tokens per step), Cn/2 = log2 (n-1)!!+ lim,-+00 Cn/2 = oo, where n!! the double factorial. This indicates that the difficulty grows without bound even when decoding only 2 tokens in parallel.
شド= [Sy] with hı
When T n/2 (2
n!!
4.2 CASE STUDY ON LIST OPERATIONS: DECODING STRATEGY PERSPECTIVE
Beyond the data distribution perspective, the practical generation quality of dLLMs critically de- pends on the decoding (unmasking) strategy. We analyze achievable accuracy under two categories: (i) Top-k (Random or Confidence): unmask & random positions or highest-confidene positions per step: (ii) Threshold (Confidence): unmask all positions exceeding confidence threshold y; if no positions meet 7, the single token with the highest confidence unmasked. We focus on an unbiased (ideal) model where each token's 's logit Ij iiii + <j. with i determined solely by the task and e, representing zero-mean stochastic noise, without intrinsic bias. We consider greedy and temperature sampling (7 1). Summary of findings Table 1.
decoding
4.2.1 TOP-K ARANDOM OR CONFIDENCE)
Shuffle Since each step the probability of correctly selecting & distinct items for the remaining positions is (i-Ikk))) the overall accuracy of successfully completing the shuffle operation is:
(n-(1-1)66=
n/l P(n - (i () (n (i 1)4j*
if = n
Acc(k: = II
DII
0
if 2 as n2 - x0,
(5)
if
regardless of using greedy decoding or temperature sampling. Notably, for both = (one-step generation) and k = 2 (two tokens per step), the accuracy converges to zero as n increases.
Replace Random Under greedy decoding (assume i: for simplicity), at each step E all (=-6--1k-1 exceeds the replace probability
k positions keep their tokens since the keep probability n-(f-1)
-ー(リ- At the final step, when >> 2, all positions are kept since k-1 > E. failing the task; when k = 2, successful replacement occurs with probability 0.5 x 0.5 + 0.5 x 0.5 = 0.5 (sum of [keep, replace] and [replace, keep)). Thus Ace(k: 2) and Acc(k
0.5.
Under temperature sampling, each position initially keeps its original token with probability 2-1 Thus, for one-step generation, we have Acc(n) = [1-1) n-1 and lim Acc(n) = !
4.2.2 THRESHOLD (CONFIDENCE)
Shuffle Assuming y > 0.5, at each timestep, the confidence for each item at each position equals
1/m where is the number of remaining masked tokens. For 2, have y > 0.5 2 1/m, so the threshold is never met when multiple tokens remain masked. Thus, only single token is decoded at each timestep, converging one-by-one decoding with guaranteed success: Acc(y 0.5) 1.
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Replace Random Under greedy decoding with n 2. each position the first timestep assigns a confidence of z=1 to retaining its original token and to replacement, thus all positions greedily preserve their original tokens. When n_س > all positions are unmasked simultancously, resulting in one-step generation that fails to perform any replacements: Acc( "== > ?) = O. When 2 = all positions fail to exceed the threshold, so only one token is unmasked per timestep. This one- by-one decoding continues through subsequent timesteps until the final step, where only a single token remains masked. At this final step, the model assigns confidence to the correct replacement, ensuring successful completion: Acc(1 m=11 1.
Table 1: Summary of findings in Section 4.
Data Distribution Perspective (Section 4.1)
Decoding Strategy Perspective (Section
Task/ / Analysis
X
litta- C(Y(X)
Ace. (Greedy. Top-k)
Acc. (Greedy l'rreshold)
Copy & Replace Index Replace Random Shuffle
0
(n () (m) logy(R 1)] x (og)(1) (ng)(n!)
(eg 1.14 00
0.5 & 2,0 Eq. (5)
1 (n
1)/R: else 0
1 > 0.5
4.2.3
EMPIRICAL VALIDATION
Acuurcy
Aocurcy
2
Am
Regiace Fund
10
Thrsshold
(a) Shuffle (T (T=B) 1) (b) Shuffle (T (c) Replace (7 1) (d) Replace (r (e) Thres. (n 10)
Figure 2: Empirical validation results on list operations: Shuffle (Figs. 2a and 2b) and Replace Random (Figs. 2c and 2d) with Random Top-k, and both tasks with Confidence Threshold (Fig. 2e).
To validate our analysis, we fine-tune LLaDA 1.5 (Zhu et al., 2025) on each list operation task and perform infilling experiments with pre-filled formatting tokens, leaving only the list item positions to be generated. Figs. 2a and 2b validate Eq. (5): accuracy converges 0 as n increases for >>> 1, with k = n converging much faster than k = 2. Fig. 2c confirms that one-step generation achieves 1/e accuracy under temperature sampling, while Fig. 2d shows that greedy decoding yields 0.5 accuracy for k = 2 but 0 for k = Fig. 2e confirms that Shuffle and Replace Random exhibit opposite trends with varying y, indicating the difficulty of achieving high accuracy for both tasks.
REALISTIC BENCHMARK: PARALLEL
While reveal limitations of parallel decoding in synthetic settings, we demonstrate that these issues persist in real-world scenarios by introducing PARALLELBENCE a realistic benchmark span- ning diverse difficulty levels to evaluate dLLMs' parallel decoding. It consists of 17 tasks across categories: (i) Waiting Line (10 tasks), (ii) Text Writing (5 tasks), and (iii) Puzzles (2 tasks).
Waiting Line Waiting Line extends synthetic list operations (e.g., Shufflle to realistic customer service scenarios. Given a queue of customers (e.g.. ["Susan Fox", "Philip Gray", "Maria Butler", "Albert Sanchez"l), the task performs queue management operations analogous to list operations. The number of customers n serves as a controllable parameter for adjusting benchmark difficulty.
Text Writing To expose the quality degradation in parallel decoding, we introduce grammar (Mor- ris, 2025) scores that impose stronger token-level dependencies. which traditional metrics such as ROUGE (Lin, 2004) cannot capture. We examine five tasks: (i) Summarization using SAMSum (Gliwa et al., 2019), (ii) Paraphrasing using Vorobev & Kuznetsov (2023), and (ii-v) our proposed Words-to- Ciai--tt--eetnnce Generation (W2S) with three difficulty levels. Both Summarization and Para- phrasing constrain outputs to rich input context, limiting token candidates and keeping C(Y)X) small. For scenarios with greater token dependencies, we propose W2S, where the goal is to con- struct sentence using the given n words, such "Construct single, coherent sentence using the

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words sand, home, play, and bottle." Since the output be freely generated using minimal input context, the token dependencies become larger depending on what output is generated. We design three difficulty levels: easy (related words), medium (loosely connected words), and hard (unrelated words), with harder variants requiring more creative construction and exhibiting larger C(Y[X).
Puzzles Ye al. (2025a;b) utilized Sudoku to demonstrate the superior planning capabilities of dLLMs over autoregressive LLMs. Crucially, every Sudoku puzzle, regardless of difficulty, has a unique solution (C(Y]X) = 0). While Latin Square (Keedwell Dénes, 2015) shares structural similarities with Sudoku, it has many valid solutions (C(YIX) > 0). We included both to examine how C(Y| X) affects parallel decoding in structurally similar tasks.
BENCHMARK RESULTS AND ANALYSIS ON PARALLELBENCH
Setup For autoregressive LLMss, Qwen2.5 3B/7B (Yang et al., 2024), Qwen3 4B (Yang et al., 2025a), and Claude 3.5 Haiku (An- thropic, 2024). For dLLMs, we test LLaDA 8B (Nie al., 2025), LLaDA 1.5 8B (Zhu al., 2025), Dream 7B (Ye et al.. 2025b), DiffuCoder (Gong et al., 2025), and closed-source Mercury (Incep- tion Labs et al., 2025). We also evaluate KV caching (Wu et al., 2025). For unmasking meth- ods, we test: i) Top-k: Random, Confidence (Chang et al., 2022), Left-to-Right', Margin (Kim et al., 2025b), Entropy (Ye et al., 2025b); and ii) Threshold: Confidence (Wu et al., 2025) with 7 {0.5, 0.6..... 1.0). We also test Factor-based (Wu et al., 2025), and semi-AR decoding (Nie et al., 2025). Further experimental details are in Appendix C. this section, we primarily focus on LLaDA 1.5, representative open-source dLLM, and four unmasking methods with results shown in Fig. 3, while full analysis including additional models, unmasking methods, and the impact of KV eaching is in Appendix D. When evaluating LLaDA 1.5 on Waiting Line, we use n (3, 4, 6), ensuring task simplicity to focus on parallel decoding effects rather than model capacity limitations.
Llama 3.1 8B, Llama 3.2 3B (Grattafiori et al., 2024),
100
10c
1C0-
122
Acoursty
Accura
Accusty
Accuraty
Acourty
C- Randen Tap-
Do videroo
16
Tokara Step
Tokama Swpp
TOAART Step
Tokana Sapp
TTkker SMep
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffle
Accursay
Acounny
Acaussy
Tokers
Tokens Step
Tooeem Step
*Tokens
Toxers Step
(f) Paraphrasing
W2S (casy)
(h) W2S (hard)
(i) Sudoku
(j) Latin Square
Figure 3: Benchmark results of LLaDA 1.5 (Zhu et al., 2025) on PARALLELBENCH: Waiting Line (Figs. 3a to 3e), Text Writing (Figs. 3f to 3h), and Puzzles (Figs. 3i and 3j).
Comparison Across Tasks For Waiting Line, Copy maintains near-perfect accuracy regardless of parallelism degree (Fig. 3a). For Reverse (Fig. 3b). accuracy varies by unmasking method. We argue that these differences stem from insufficient model capacity rather than token depen- dency (C(YIX) 0). Replace Index (Fig. 3c) and Replace Random (Fig. 3d) exhibit contrasting trends. Despite Replace Random achieving near-perfect one-by-one decoding accuracy compared to Replace Index's 's below 50% accuracy, this advantage reverses under parallelization: Replace In- dex maintains stable accuracy with increasing parallelism, while Replace Random degrades rapidly across all unmasking methods. This reversal aligns with Section 4: C(Y 0 for Replace Index but C( > 0 for Replace Random. Shuffle (Fig. 3e) shows the steepest accuracy degradation, dropping from pear-perfect zero more rapidly than Replace Random as parallelism increases. For
Unmasks & tokens at time from left right.
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Text Writing (Figs. 3f to 3h), all tasks achieve near- near-perfect grammar scores with one-by-one decod- ing, but degrade at increasingly steep rates under parallelization: Paraphrasing. W2S (easy), then W2S (hard). This aligns with expected conditional dependencies. Paraphrasing merely restructures existing content with rich context, limiting token candidates and keeping C( small. Conversely, W2S tasks generate complete sentences from sparse word constraints, expanding the candidate space where each position strongly influences others. W2S (hard) uses semantically unrelated words re- quiring more creative construction than W2S (easy)'s 's naturally coherent word sets, resulting in larger CXY and steeper degradation. For Puzzles (Figs. 3i and 3j), Latin Square outperforms the harder Sudoku under one-by-one decoding, but this advantage disappears with increased parallelism (Latin Square: C(Y X) > 0, Sudoku: C(Y[X) = 0), leading to similar accuracy.
Comparison Across Unmasking Methods Confidence Threshold outperforms Top-k at conserva- tive thresholds through adaptive token selection, but suffers rapid degradation at aggressive thresh- olds due to unpredictable unmasking spikes, making careful tuning essential. When comparing among top-k methods, for Reverse and Replace Index, Confudence Top-k outperforms Random Top-k. This is because when X() = O, model imperfection limits accuracy, making it beneficial to un- mask tokens that the model is confident about first. For Replace Random and Shuffle (C(Y) X)) > 0), Random Top-k conversely outperforms Confidence Top-k. In conclusion, no universally superior unmasking method exists, with performance varying by task.
Semi-AR Decoding Results Semi-AR decoding controls the left-to-right tendency in unmasking order by adjusting block length. Its effectiveness in parallel decoding depends the dependency structure. With local dependencies (e.g., grammatical constraints in Text Writing), small blocks enforce left-to-right (local) decoding, causing quality degradation. With global dependencies (e.g., Waiting Line's 's distributed items), left-to-right decoding becomes beneficial by capturing formatting tokens around items. Fig. 5 shows different accuracy trends between Text Writing and Waiting Line across block sizes (Random Top-2), indicating the difficulty of optimizing both tasks simultancously.
Accunsyy
Accunsay
Ascussyy
necurss
Names Quostion
Question
NNames
Names Quostion
NName Quession
(a) Mercury
(b) Haiku 3.5
(c) Qwen2.5 3B
(d) Qwen3 4B
(c) Qwen2.5 7B
Figure 4: Waiting Line results on Mercury (Inception Labs et al., 2025) and autoregressive LLMs.
Performance of Mercury vs. Autoregressive LLMs Fig. 4 shows Waiting Line results with n E [5, 20), where Mercury and autoregressive LLMs show opposite accuracy trends on Reverse and Shuffle. As Reverse seems harder (requiring exact reversal) than Shuffe (accepting any per- mutation), autoregressive LLMs score higher on Shuffl. However, Mercury shows the opposite: it maintains near-perfect accuracy on Reverse but fails with Shuffle, with accuracy dropping sharply as n increases, consistent with Section 4. This indicates that the closed-source Mercury struggles to adaptively adjust its parallelism to maintain quality on tasks with high token dependencies.
Broad Coverage of PARALLELBENCH Fig. 6 demonstrates BARALLELBENCHE necessity and differentiation from existing benchmarks. The x-axis shows waallelism-inddcee quality degrada- tion (rightward = greater). while the y-axis shows semi-AR block length effects (upward = better quality with left-to-right ordering). For Waiting Line, tasks with C(Y]X) = appear left, while those with C(Y > O progressively move rightward with increasing degradation, culminating in Shuffle at the far right. For Text Writing, lower dependency tasks (paraphrasing, summarization) appear left, while higher dependency W25 tasks appear right. In contrast to existing benchmarks like GSM8K (Cobbe et al., 2021). MATH (Hendrycks et al., 2021), and IFEval (Zhou et al., 2023), which occupy narrow range, PARALLELBENCH spans broad spectrum of parallel decoding diffi- culty. This broad coverage uniquely enables the evaluation of adaptive methods' ability to modulate parallelism according task difficulty. Details are in Appendix F.
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Order Preference (key Leff Fight
BSM MCH
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Figure 5: Semi-AR results on Waiting Line and Text Writing.
Figure 6: Broad coverage of Figure 7: Speed-quality trade- BARALLELBENCII.
off with oracle performance.
Speed-Quality Trade-off' with Oracle Performance Fig. 7 shows the speed-quality trade-off curves for each unmasking method. Static unmasking (top-k) methods show dramatic accuracy drops as offs. This raises the question: Do existing adaptive unmasking methods already provide sufficient speedup-quality trade-offs? To answer this, measure oracle performance: the best possible trade-off assuming access to the optimal threshold for each sample that yields the correct answer. The oracle achieves both the best accuracy and significant speedup over threshold methods with comparable accuracy, demonstrating that per-sample threshold adaptation alone yields significant improvements and suggests substantial room for future research. Details are in Appendix F.2.
increase, while adaptive unmasking (threshold) achieves superior trade-
Takeaway. Static parallel decoding (e.g., top-k) can suffer severe quality degradation, and adaptive decoding strategies (e.g., threshold) still have significant room for improvement.
7 EXPLORING ADDITIONAL TECHNIQUES
100
Repiaca
Hausaco Hone.
rocuraty Rt
Accincy
Pocurncy
124
10
144
15
124
124
15
22
12.4
10
Toxwes per Step
Tokerss per Step
Tokeme per Step
Tokens per Step
Tokees pET Step
(a) Pretrained
(b) Fine-tuning
(c) Chain-of -hoouhh
(d) ReMDM
(e) RCR
Figure& 8: Waiting Line results using LLLDA 1.5 (Random Top-k) with various advanced techniques.
We further explore whether benchmark performance can be improved when various advanced tech- niques for dLLMs are applied. Details and full results in Appendix E.
Additional Unmasking Methods Beyond the methods evaluated in our main experiments, several recent works (Ben-Hamu al., 2025; Luxembourg et al., 2025; Wei et al., 2025; Huang al., 2025) propose advanced unmasking strategies to improve performance in dLLMs. For an overview of these methods, see Appendix 1. We evaluate their speed- quality trade-offs on PARALLELBENCH and report results in Appendix E.
Fine-tuning We fine-tuned LLaDA 1.5 on Waiting Line to examine whether fine-tuning improves parallel decoding performance (Figs. 8a and 8b). One-by-one decoding achieves near 100% accu- racy for all tasks after fine-tuning, including Replace Index, which improves from below 50% to nearly 100%. Notably, Replace Index maintains high accuracy even with parallel decoding, con- firming that ideal models can accurately learn the target distribution under parallel generation when C(Y]X) 0. However, Replace Random and Shuffle still degrade with parallel decoding, support- ing Section that even an ideal model cannot resolve parallel decoding limitations for C() > 0. Details and full results are in Appendix E.2.

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Published as a conference paper at ICLR 2026
Chain-of-Thouur Thought Prompting (CoT) Figs. 8a and 8c show that CoT mitigates quality degrada- tion under increased parallelism by generating intermediate reasoning steps that reduce inter-toker dependencies in final answers. However, due to using 8x more output tokens. CoT cannot serve as a fundamental solution for improving the speed-accuracy trade-off under parallel decoding. Details and full results provided in Appendix E.3.
Remasking Samplers Most dLLMs use masked diffusion, where tokens unmasked in previous timesteps cannot be refined later. However, this prevents correcting inaccurate predictions from early timesteps, leading to quality degradation. Recent training-fre samplers, such as ReMDM (Wang al., 2025) and RCR (He et al., 2025), enable remasking for masked diffusion models. However, our tests on Waiting Line show no improvements, revealing limitations of training-free approaches. More recently, several works (Zhang et al., 2025; Kim et al., 2025a) demonstrate that finetuning dLLMs to support remasking can further improve performance. Details are in Appendix E.4.
Discrete Diffusion with Uniform Transition Matrix Unlike masked diffusion, discrete diffusion with uniform transition matrix enables iterative refinement of all tokens throughout the denoising process, potentially correcting errors from conditional independence assumptions in parallel decod- ing. We test this by fine-tuning masked and uniform diffusion models from SEDD (Lou et al., 2024). See Appendix E.5 for details and full results.
CONCLUSION
This paper investigates the trade-off's of parallel decoding in dLLMs. We provide an information- theoretic analysis and conduct case studies using synthetic list operations, examining both data dis- tribution and decoding strategy perspectives to reveal quantitative insights into the limitations of parallel decoding. Building these findings, we propose PARALLEL demonstrating that limitations observed in synthetic scenarios similarly manifest in real-world ap- plications. Using our benchmark, we draw two key conclusions: (1) dLLMs with parallel decoding can suffer severe quality degradation in real-world scenarios, and (2) existing decoding strategies fail to adaptively adjust parallelism based on task difficulty for optimal speed-quality trade-offs.
a new benchmark
Limitations and Future Works First, while our benchmark comprises 3 realistic categories and 17 tasks, broader coverage of real-world scenarios would be beneficial. Second, primarily alyzed short output sequences to focus on fundamental characteristics, and tasks requiring longer sequences may yield different results. While our adjustable-length tasks naturally support longer sequence evaluation and we provide a preliminary analysis in Appendix D.5, more thorough study remains an important direction for future work. Finally, leveraging PARALLEL BEnCH to develop novel unmasking methods that address current parallel decoding limitations is an important goal.
ACKNOWLEDGMENT
Kangwook Lee is supported by NSF Award DMM-20032399, NSF CAREER Award CCF-2339978, Amazon Research Award, and a grant from FuriosaAl.
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Appendix
Mathematical Proofs
16
A.1 Proof of Theorem
16
A.2 Proof of Theorem 2
16
A.3 Extended Version of Theorem 2
17
Further Discussion on Related Work
18
B.1 Additional Unmasking Methods
18
B.2 Related Benchmarks
18
B.3 Discrete Diffusion Strategies
19
Benchmark Dataset Specifications and Evaluation Details
19
Additional Experimental Results
22
D.I Unmasking Strategies: Margin Top-k and Entropy Top-k
22
D.2 Factor-based Unmasking
23
D.3 Impact of KV Caching
23
D.4 Semi-autoregrrssivve Decoding
24
................................
D.5
Benchmark Results on Longer Outputs
................................
25
D.6
Benchmark Results with Additional Metries
25
Additional Techniques
26
E.1
Benchmark Results on Additional Parallel Decoding Methods ................................
26
E,2
Impact of Fine-tuning
26
E,3 Chain-of-Thought (Co'T) Prompting
27
E,4
Remasking Samplers: RCR and ReMDM
28
E.5
Discrete Diffusion with Uniform Transition Matrix
29
F
Task Characterization
29
F.I
Characterizing Tasks by Parallelizability and Decoding Order
29
F2
Speed-Quality Trade-off
30
F3
Speed-Quality Trade-off in Existing Benchmarks
31
F44
Time-Quality Trade-off
31
Failure Cases
32
H
Comprehensive Experimental Results
32
H.1 Comparison with Large Language Models
32
H.2
Complete Benchmark Results.
34
Autoregressive LLM Parallel Decoding
34
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A MATHEMATICAL PROOFS
A.1 PROOF OF THEOREM 1
Proof. The 7'step parallel decoding model is defined by the factorization:
T II (o
X)
(6)
==1
Similarly, we can decompose the true data distribution according to the partition {5:)?-1:
T
Panta (YI))=
II
Paata ( [S: Sci)
(7)
==1
Substituting these decompositions into the KL divergence formula, we get:
DKL. (Panta
(VI)) II Po(Y(X))
Panaa Pama(YY (YIX)
Pum
log
(8)
(Y
I1 Panta Sex))
Pam
log
(9)
II Po(S, Sei)
Patnn ( S X, Scx))
E
log
(10)
Po Xx,
Ese 1SerrPau Puus [DKI. (Rkx.(Puu (Paata (5, ( P(())X
(11)
At each step the model assumes conditional independence among the tokens in S; given the context (X, Sx),, such that (S, Sex) II,,es, Po XX Sei). Therefore, by applying Eq. (1) from Section 3, we have:
DEL (Pataa (S,
||
2 S<s
(12)
By substituting this lower bound back into our sum, we have:
ming (Panuu
(Y|X) X)(
T
= mins
E Pan
(DL (P (,(
(13)
Es Ese Pan [mino, DKL. (Pauaa (S.
Po Sc:))
(14)
Σ Es Pam Pam. [C(S))x,Se.))
(15)
This completes the proof.
A.2 PROOF OF THEOREM 2
Lemma 1 (Subadditivity of Conditional Total Correlation). Let a set of random variables S be partitioned into two disjoint subsets A and B (i.e., S AU B). For any conditioning context 7, the conditional total correlation of S is lower-bounded as follows:
C(SIZ) C(A(Z) + EA- ( C( 7, 2, A)]
(16)
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Proof of Lemma 1. Using the definition of conditional total correlation (C(SIZ) Eyes H))
(S )), we have:
C(A|Z) Ba(c(BIZ,
=E (vaa ((A))) Σ (( - H
(17)
V.EA
WoEB
Σ H(ya H(A Σ
- (()),
(since Hy))Z) 2 H3bolZ,
V.EA
BoEB
(18)
Σ
Hyy + Σ H()ll))
(H(A + H(B),AA
(19)
BAEA
EB
Σ (A, (by the chain rule of entropy) VES
(20)
= -C(S)Z)
(21)
This completes the proof.
Proof of Theorem 2. Let {5 be an optimal T'step partition that achieves the minimum error bound Cy. We construct a (T + 1)-step partition { 7- by splitting the last set of the optimal partition, Sy. into two non-empty, disjoint subsets and (i.e., St. A U B). The new partition is {Si ................................ -1 A, B), and we have:
C ((()))
(22)
Σ
(23)
Str: A)]
(by Lemma 1)
(24)
(by Theorem
(25)
2 ss 2111 (1SA
(26)
L7++
(27)
Thus, we have Li 2 CT+1
A.3 EXTENDED VERSION OF THEOREM
Theorem 3 (Monotonicity of Error Bounds for Input-Dependen Partitions), For any given input
X, let Cr( (X) be the error bound specific T-step partition {5:)
=
(XSS (x | Sc:)]
(28)
The optimal T-step enoor bound, Li, is the expected value of the minimum error bound over all possible partitions for each input:
C = Ex-Pam mmins.... Cr((S))T_
Then Ci is monotonically decreasing with respect to the number of generation steps:
C 2 Cr+1
(29)
Proof of Theorem 3. We begin by establishing a pointwise inequality for any single, arbitrary input Let consider special data distribution concentrated entirely this single input a.
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Applying the conclusion of Theorem 2 to this special case directly establishes the following rela- tionship. The optimal T-step error for this distribution (which is simply the optimal error for the input z) is greater than or equal to the optimal sTel)- error:
min Lr (r( (x) 2 min (S)TT) LT+ (1S)
(30)
Taking the expectation of this pointwise inequality Eq. (30) over the true data distribution X Paata directly yields the final result:
5T: :xx [min(s)), Lr (r((S)) 2 Ex min [ LT+ (15))
LT++
Thus, have Lj 2 -T+11
B FURTHER DISCUSSION ON RELATED WORK
B. ADDITIONAL UNMASKING METHODS
Recent work on dLLMs has focused on optimizing the unmasking process to improve inference efficiency and generation quality. Besides the unmasking methods studied in this work, several additional methods (Ben-Hamu et al., 2025; Luxembourg et al., 2025; Wei et al., 2025; Huang et al., 2025; Wu & Zhang, 2025; Israel et al., 2025) target acceleration through parallel decoding. For instance, the EB-Sampler (Ben-Hamu et al., 2025) adaptively unmasks the largest group of tokens whose cumulative entropy falls below threshold, 7, achieving a 2-3x speedup. Similarly, the Dilated Unmasking Scheduler (DUS) (Luxembourg et al., 2025) uses deterministic, coarse-to-fine schedule to unmask non-adjacent tokens, reducing the number of denoiser calls within a block of size B from O(B) to (log B). The SlowFast Sampling (Wei al., 2025) alternates between slow, exploratory phases and fast, parallel decoding phases, yielding up to 15.6x speedup. Other works focus on generation quality. The PC-Sampler (Huang al., 2025), for example, corrects for biases in uncertainty-bast based sampling by using a composite score that combines a position-awar weight with frequency-call callbratee confidence score, improving performance by over 10%.
B.2 RELATED BENCHMARKS
To contextualize our work, we review several key benchmarks commonly used to evaluate the capa- bilities of LLMs across different domains.
The Grade School Math 8K (GSM8K) dataset (Cobbe et al., 2021) is prominent bench- mark designed to assess the multi-step mathematical reasoming abilities of LLMs. It consists of thousands of grade-school- word problems that require sequence of logical steps and arith- metic operations to solve. The primary evaluation metric is final answer accuracy, where the model's generated solution must exactly match the correct numerical result. Success on GSMSK is consid- ered strong indicator of model's capacity for complex, chain-of-thoughi reasoning.
GSM8K
HumanEval The HumanEval benchmark (Chen et al., 2021) is standard for evaluating the code generation capabilities of models. The task involves completing Python function bodies based on a given function signature and descriptive doestring. The dataset contains 164 such programming challenges of varying difficulty. Performance is measured by functional correctness, typically using the pass @ (Chen et al., 2021) metric.
SAMSum The SAMSum dataset (Gliwa et al., 2019) tailored for the task of abstractive sum- marization of natural, real-world dialogues. It contains short, informal conversations, requiring model to produce a concise summary that captures the main points of the exchange. The standard evaluation protocol relies on the ROUGE score (Lin, 2004), which measures the n-gram overlap be- tween the model-generated summary and one or more human-written reference summaries. While ROUGE is effective for assessing content overlap, work diverges by focusing the grammat- ical correctness and fluency the generated summaries, aspects of quality not fully captured by lexical metrics.
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ChatGPT-Paraphrass The ChatGPT-Paraphhrase Paraphrases dataset (Vorobev & Kuznetsov, 2023) is de- signed for evaluating a model's ability to rephrase sentences while preserving their original semantic meaning. The dataset provides pairs of original sentences and their corresponding paraphrases. This benchmark is crucial for assessing model's fine-grained understanding of language and its capac- ity for fluent and diverse text generation, which processing applications. While standard evaluations for this task often rely on semantic similarity metries, our approach is different. Similar SAMSum, are primarily interested in the grammat- ical evaluation of the output.
skills for sophisticated natural language
B.3 DISCRETE DIFFUSION STRATEGIES
In discrete diffusion, common strategy is the absorbing state approach, also known as masked diffusion. This method corrupts data by progressively replacing original tokens with a single, special [MASK] token. The key advantage of this technique lies in its reverse process. The model's task is simplified to "filling in the blanks" at known [MASK] locations, which provides a very direct and clear learning signal. This is the primary approach used by many prominent open-source models, such as LLaDA (Nie et al., 2025) and Dream (Ye et al., 2025b).
In contrast, the uniform transition approach corrupts data differently. Instead of using special token, it substitutes an existing token with any other token from the vocabulary, with each possi- bility having an equal probability of occurrence. This method gradually transforms the input into sequence of purely random tokens. Consequently, the reverse process is more complex: the model must predict the original token from noisy, corrupted one, rather than from a designated blank slate. Some recent models, including SEDD (Lou et al., 2024), have explored this uniform approach.
C BENCHMARK DATASET SPECIFICATIONS AND EVALUATION DETAILS
Table 2: Benchmark tasks and evaluation metrics BARALLELBENCH.
Category
Task
#Samples
Metric
Copy
100
Accuracy
Sort
100
Accuracy
Reverse
100
Accuracy
Shuffle
100
Accuracy
Waiting Line
Replace Index
100
Accuracy
(one-shot)
Replace Random
100
Accuracy
Insert Index
100
Accuracy
Insert Random
100
Accuracy
Remove Index
100
Accuracy
Remove Random
100
Accuracy
Summarization
100
Grammar, Rouge-L
Paraphrasing
100
Grammar, BERTScore, BLEU)
Text Writing
Words-to-Sents teret-t-eeeee (casy)
100
Grammar, Accuracy
(zero-shot)
Words-to-Sentence (medium)
Grammar, Accuracy
-ords--t-SSeneence (hard)
100
Grammar, Accuracy
Puzzle
Latin Square (4x4)
100
Accuracy
(one-shot)
Sudoku (4x4)
108
Accuracy
Table 2 provides comprehensive overview of PARALLELBENCH, We omit the synthetic list oper- ations from this discussion, as their setup is analogous to the Waiting Line tasks. Example prompts and corresponding answers for each task are presented in Table 3.
Evaluation Details For the Waiting Line and Puzzle tasks, which are relatively unfamiliar to the models, we employ one-shot prompting. In this setting, the model is first presented with a complete example (a prompt and its corresponding solution) before being given the actual test prompt. In contrast, for Text Writing tasks, standard zero-shot prompting.
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All models evaluated using greedy decoding, with the exception of infilling tasks, for which use temperature sampling with a temperature of 1.0. The maximum number generated tokens is set to 32 for Waiting Line and 64 for both Puzzle and Text Writing.
Evaluation Metries For the Waiting Line and Puzzle tasks, we use accuracy, defined as binary score indicating whether the generated output exactly matches one of the valid solutions. For the Text Writing benchmarks, we employ several scores consisting of a base gramiar score and tasc-spec metries. The grammar score, evaluated using the tool from Morris (2025), is for grammatically cor- rect outputs and 0 otherwise. The task-specific metrics are as follows: For Summarization, we report ROUGE-I (Lin, 2004) against reference summary. For Paraphrasing, we measure both semantic similarity using BERTScore (Zhang et al., 2019) and lexical diversity using BLEU (Papineni et al., 2002) to penalize outputs that are too close to the original sentence. For inclusion accuracy metric that verifies if all requested words present in the generated sentence. For simplicity, we primarily report the grammar score in the main body of the paper. A comprehensive breakdown of all metries available in Appendix H.I.
Dataset Generation The tasks for our benchmark were sourced and generated as follows. For Waiting Line, we created lists by randomly sampling from a predefined list of first and last names, which were generated with Gemini 2.5 Pro (Google Deepmind, 2025). For Latin Square, we gener- ated prompts requesting the creation of Latin squares of size 4x4 with random symbols. For Sudoku, used the existing dataset from Ye et al. (2025b). For Summarization and Paraphrasing, we uti- lized 100 examples of the existing SAMSum (Gliwa et al., 2019) and Vorobev Kuznetsov (2023) used Gemini 2.5 Pro to generate word
benchmarks, respectively. Finally, for Words-to-Sentence sets of four words at three difficulty levels: easy (simple, semantically aligned words), medium (more complex but aligned words), and hard (complex words that challenging connect mean- ingfully).
Table 3: Benchmark prompts and examples. Bold indicates the input part of the prompt.
Task
Prompt
Example Answer
Copy
You are managing waiting line at customer service desk. You need record the following people the order they arrived: Biillyy Ramos", "Alan Wells", *Grace Wright") Please copy the list exactly and provide only the final list.
[BBllly Ramos", "Alan Wells". "Grace Wright"]
Sort
You are managing a waiting line at a customer service desk. The following people should be organized alphabetically by last name for efficient processing: ["David Lewis", "Patrick Tran", "Sean Diaz"] Please sort the list alphabetical order and provide only the final list.
["David Lewis", "Patrick Tran", "Sean Diaz"]
Reverse
You are managing a waiting line at a customer service desk. The previous staff member put the waiting line in the wrong order. Please reverse the order of the following people in the waiting line to correct it: ["Mark Richardson", "Kevin Martinez", "Henry Young"] Please reverse the order of the list and provide only the final list.
("Henry Young". "Kevin Martinez", "Mark Richardson"]
Shuffle
You are managing a waiting line at a customer service desk. The waiting line should be randomly shuffled distribution: ["Paul Payne", "Robert Riley"", "Peter Stone") Please randomly shuffle the list and provide only the final list. Ensure the sequence is different from the original.
["Robert Riley", "Paul Payne", "Peter Stone")
fair service
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Task
Prompt
Example Answer
Replace Index
You are managing waiting line at customer service desk. The person position 0 must be replaced with "Henry Warren": P Morgan", "Erie King", "Joe Reed""] Please replace the person at the specified position with "Henry Warren" and provide only the final list.
("Henry Warren", "Eric King". "Joe Reed")
Replace Random
You are managing waiting line at customer service desk. One person in the waiting line must be replaced with "Juan Torres": [*David Owens", "Kelly Payne", "Aaron Freeman"] Please replace one random person with "Juan Torres" and provide only the final list.
D"David Owens", "Kelly Payne", "Juan Torres"]
Insert Index
You are managing a waiting line at customer service desk. A new person "Aaron Stewart" is inserted into the line position 2: (*Charlotte Chavez", "Grace Baker", "Keith Cooper"] Please put the new person at the specified position and provide only the final list.
["Charlotte Chavez", "Grace Baker", "Aaron Stewart", "Keith Cooper"]
Insert Random
You are managing a waiting line at a customer service desk. A new person "Justin McDonald" is inserted into the line at random position: ["Johnny Sullivan", "Ryan Baker", "Juan Wilson") Please put the new person the random position and provide only the final list.
["Justin McDonald", "Johnny Sullivan", "Ryan Baker", "Juan Wilson"1
Remove Index
You are managing a waiting line at customer service desk. The person position 2 has left the waiting line: ["Sarah Robertson", "Maria Mitchell", "Donald Hughes"] Please remove person the specified position and provide only the final list.
("Sarah Robertson", "Maria Mitchell")
Remove Random
You are managing waiting line at customer service desk. One person has left the waiting line: ["Karen Kim",, "Jerry Hall", "Jose Marshall"] Please remove random person and provide only the final list.
["Jerry Hall", "Jose Marshall"]
Summarization
Summarize the following conversation. Only output the final result. Steve: Bought the new Dream Theater album 5 minutes ago. hope it's good. Rob: have it here on desk, ready for the first listening. Steve: Ok, I'll tell you later what I think about it. Rob: Same here. See you later! Summary:
Steve and Rob will talk about new Dream Theater album, after they finish listening.
Paraphrasing
Paraphrase the following sentence. Only output final result. Sentence; Any idea what sweater this is? Paraphrase:
Can you identify this sweater?
Hords-to-Sentence
Construct single, coherent sentence using the words dog, park, ball, and throw.
love to throw the ball for my dog at the park.
(casy)
Words-to-Sentence (medium)
Construct single, coherent sentence using the words apple, river, table, and happy.
was so happy to sit at the table by the river and cat crisp apple.
Words-to to-Setence (hard)
Construct single, coherent sentence using the words algorithm, river, symphony, and moss.
The growth of the moss along the river bank seemed follow natural algorithm, quiet symphony of life unfolding.
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Task
Prompt
Example Answer
Latin Square (4x4)
Generate Latin square of size 4 with the symbols [H, 4, C, AJ. Only output the final result as CSV.
H,4.A.C C,A.4.H A.H.C,,4
Sudoku (4x4)
Fill the positions where the values are 0 in 4x4 grid with digits so that each column, each row, and each of the four 2x2 subgrids that compose the grid contains all of the digits from to 4. Input: 0042 2031 4023 3214 Output:
1342 2431 4123 3214
D ADDITIONAL EXPERIMENTAL RESULTS
D.1 UNMASKING STRATEGIES: MARGIN ToP-K AND ENTROPY TOP-K
Vage
Taare deap
Talnn Shop
Taure Stap
Saone per Stop
Taars Ship
Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
Shuffle
TAAYA Sepp
Talne Seop
Tavis Shop
SAve Seap
(f) Insert Index
(g) Insert Random
(h) Remove Index
(i) Remove Random
( Sort
Figure 9: Full Waiting Line (n 3, 4, 6) results using LLaDA 1.5 (Zhu et al., 2025) with Margin Top-k and Entropy Top-k.
Tpp
Taare Sep
Taknn Stop
Tanne Sepp
Saane per Stop
Taans Ship
(a) Paraphrasing
(b) Summarization
(c) W2S (easy)
(d) W2S (medium)
(e) W2S (hard)
Figure 10: Full Text Writing results using LLaDA 1.5 (Zhu et al., 2025) with Margin Top-k and Entropy Top-k.
Recently, two alternatives to confidence-based unmasking have been proposed: Margin Top-k (Kim et al., 2025b) and Entropy Top-k (Ye et al., 2025b). These methods function similarly by iteratively revealing tokens but employ different metrics to quantify model uncertainty.
Margin Top-k calculates the score as the difference between the probabilities of the two most likely token candidates, P1 and p2. The margin, m = P1 P2, is large when the model highly confident in single token, and small when there ambiguity between the top candidates.
Entropy Top-k, contrast, uses the Shannon entropy of the entire output probability distribution to measure uncertainty. A low entropy value signifies peaked, high-confidence distribution, whereas a high entropy value indicates more uniform and uncertain distribution.
We compare both approaches against Confidence Top-k in Fig. 9 and Fig. 10 to evaluate their rela- tive performance. In our experiments, Margin Top-k and Entropy Top-k yield perform similarly to Confidence Top-k.
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D.2 FACTOR-BASED UNMASKING
Acquacy
Car Cereeces Tershod
Shap
Shp
TTars Stp
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffle
Shop
deop
Yaccns Shop
(I) Insert Index
(g) Insert Random
(h) Remove Index
(i) Remove Random
(j) Sort
Figure 11: Full Waiting Line (n = 3, 4, 5, 6) results using LLaDA 1.5 (Zhu et al., 2025) with Factor- based unmasking.
100-
124
(a) Paraphrasing (b) Summarization
(c) W2S (easy)
(d) W2S (medium)
(c) W2S (hard)
Figure 12: Full Text Writing results using LLaDA 1.5 (Zhu et al., 2025) with factor-based unmask- ing.
Factor-based unmasking (Wu et al., 2025) is an adaptive method for determining how many tokens to decode in parallel during inference. After calculating the confidence scores for potential next tokens, the scores are sorted in descending order. The strategy then selects the largest number of tokens, n, that satisfies the condition:
(n 1)(1-e(n)) - c(n)) < f
Here, c(n) represents the confidence of the n-th token in the sorted list, and f is a predefined hyperparameter.
In contrast to Threshold-based unmasking, which accepts any token whose individual confidence exceeds fixed value Factor-based is dynamic. It evaluates tokens group, allowing the degree of parallelism to increase when the model is highly confident and decrease when it is not.
In Fig. 11 and Fig. 12 compare Factor-based based unmasking with Threshold-basee unmasking with the following values for f E (0.7, 1.0, 1.3, 1.6, 1.9]. The results show that Factor-based unmasking follows similar trend compared to Threshold-baa of the number of tokens per step in general.
unmasking. However, it has narrower range
D.3 IMPACT OF KV CACHING
Unlike autoregressive L.Mss, dLLMMs cannot effectively utilize KV cache, causing significant la- tency at each timestep. Recent training-fres KV cache methods (Wu et al., 2025) claim dramatic speedups with minimal accuracy loss on benchmarks like GSM8K (Cobbe et al., 2021) and Hu- manEval (Chen et al., 2021). In Fig. 13 we evaluate whether PrefixCache from Fast-dLLM (Wu et al., 2025), maintains effectiveness on PARALLELBENCE under parallel decoding. The results show that caching decreased accuracy in general. Nevertheless it maintains similar trend to no caching where parallel decoding decreases performance. Complete results for PrefixCache are in Fig. 32.
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Contidence Threshold PrefeCaahh No Cacha
Acqurcyy
60
Accuracy
62
Acourccy
8
88
12
18
12
18
12
18
Tokena Ship
Tokana per Stip
Tokena Shop
(a) Replace Index
(b) Replace Random
(c) Shuffle
Figure 13: Fast-dLLM results on Repluce Index, Replace Random, and Shuffle using PrefixCache.
D.4 SEMI-AUTOREGRESSIVEE DECODING
Semi-autoreerrsssive decoding partitions the input sequence into blocks of equal length. These blocks are processed sequentially from left to right, while the tokens within each individual block decoded in parallel. In the edge case where the block length is one, this process becomes equiv- alent to standard autoregressive decoding, generating a single token at a time. We investigate the impact of varying block lengths performance for several unmasking methods, fixing the number of tokens decoded in parallel to (Figs. 14 and 15).
In Text Writing tasks, performance improves block length increases. This suggests that global dependencies are crucial for grammatical correctness, whereas smaller blocks often lead to errors and lower scores. Conversely, the Waiting Line tasks show opposite trend. Here, left-to-right (de- coding length 2) enhances performance by leveraging local dependencies to better match formatting tokens with the surrounding content.
CD
Slct
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(e) Shuffle
(I) Insert Index
(g) Insert Random
(h) Remove Index
(i) Remove Random
(j) Sort
Figure 14: Full Waiting Line (n 3. 5, 6) results using LLaDA 1.5 (Zhu al., 2025) with semi- autoregressive decoding (k- = 2).
Accuney
Scence
Book Langh
Book Lergle
300 Lenge
50 Logg
00ck Larg
(a) Paraphrasing
Summarization
(c) WW2 (casy)
(d) W2S (medium)
(c) W2S (hard)
Figure 15: Full Text Writing results using LLaDA 1.5 (Zhu et al., 2025) with semi aomi-autoregressvve decoding 2).
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D.5 BENCHMARK RESULTS ON LONGER OUTPUTS
We intentionally focus on outrt- settings to isolate the effects of parallel decoding from model capacity limitations. In practice, even SOTA open-source dLLMs such as LLaDA and Dream achieve only around 50% one-by-one decoding accuracy on Waiting Line tasks when n increases, despite these tasks being conceptually simple. This indicates that longer outputs quickly introduce capacity bottlenecks that would confound our analysis. Importantly, PARALLELBENCH is designed so that output length can be freely adjusted through hyperparameters, enabling longer-output evalu- ations future, higher-capacity dLLMs become available.
For completeness, we also report results on longer outputs. For Waiting Line, we increase n from {3, 4,5, 6) to {21, 22, 23, 24] and the max generation length from 32 to 128. For Paraphrasing, use the XSum dataset and increase the generation limit from 64 to 256. For Wordssto-Sentence, we expand from single-sentence generation (n to ten-sentence generation (n 7), increasing the generation limit from 64 to 256.
As shown, except for very simple tasks such as Copy, one-by-one decoding already performs poorly in longer-output settings. Furthermore, even Copy undergoes sharp degradation as parallelism in- creases, while other tasks rapidly collapse near-zero accuracy. For Text Writing tasks, both Para- phrasing and Fords-to-Sentenc similarly converge toward near-zero accuracy as parallelism in- creases. This suggests that limited model capacity significantly amplifies parallel decoding degra- dation for longer outputs.
120
10c
ACCUST 12
Accrsty
Conkderds Teau
Accusty
ACCU
Contderza Thisshole
Takana Stip
Tokans Swp
Tokans Shop
Tokkmns Skip
Tokama Stpp
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffle
10c
122
Acoustty
Accuraty
Actursty
Accuraty
Acourty
Takema Step
Tokamn Swpp
TokAET Slep
Tokkmt
Siep
Tokker Step
(f) Insert Index
(g) Insert Random
(h) Remove Index
(i) Remove Random
(i) Sort
Figure 16: Longer Waiting Line (n 21, 22, 23, 24) results using LLaDA 1.5 (Zhu et al., 2025).
Accuray
Aczurayy
Azzuraay
53
21
35
35
Tokens
*Tokens
Tooeess
(a) Paraphrasing
(b) W2S (easy)
(c) W2S (medium)
(d) W2S (hard)
Figure 17: Longer Text Writing results using LLaDA 1.5 (Zhu et al., 2025).
D.6 BENCHMARK RESULTS WITH ADDITIONAL METRICS
For Text Writing tasks, we also report the BERTScore (Zhang et al., 2019), ROUGE-L (Lin, 2004), and Inclusion Accuracy metrics introduced in Appendix C. BERTScore and ROUGE-L are substan- tially less sensitive to parallelism, showing only mild degradation as the number of tokens per step increases. By contrast, inclusion accuracy behaves similarly the standard accuracy metric: as par- allelism increases, models increasingly fail to include all required content, leading to a clear decline in inclusion accuracy.
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100
100
Pocusonnnccoo Accuraty 12
incherson Accuraae
100
Incusion Actuma
100
ROUGE
Go karss llrruaal)
# Tokonss per Stop
Tokons Stop
Toxens 3top
Tokons Shop
Tokons 201 3t5
(a) Summarization
(b) Paraphrasing
(c) W2S (casy)
(d) W2S (medium)
(c) W2S (hard)
Figure 18: Benchmark results with additional metries using LLaDA 1.5 (Zhu al., 2025). We use ROUGE-L for Summarization, BERTScore for Paraphrasing, and an inclusion accuracy for W2S.
E ADDITIONAL TECHNIQUES
E.1 BENCHMARK RESULTS ON ADDITIONAL PARALLEL DECODING METHODS
We benchmark the speed-quality trade-offs of the newly released methods SlowFast Sampling (Wei et al., 2025), DUS (Luxembourg et al., 2025), WINO (Hong et al., 2025), and APD (Israel et al., 2025). Since APD currently supports only Dream, we report results for APD on Dream 7B and the rest LLaDA 1.5.
Flst Sampling and DUS show worse trade-off curves than the soffidence-threshole method on PARALLELBENCH whereas WINO shows better curve, indicating emerging progress toward intelligent parallel decoding. However, all remain far below the oracle, leaving substantial room for improvement. For APD, performance surpasses the theeese method at high parallelism but falls short of it at low parallelism, again suggesting considerable room for future advances.
100
Top-k
100
Top-t
Leftto-Aigh Top-k
Lehrio-Right Top-k
Top-k
Confidenie Top-k
Donfidionee Threshoid
Confidonde Threshold
80
DUS
80
SlowFast Sampling
* Dracie
WIND
Oradie
Accuracy
60
Accuracy
60
40
40
20
0
10
15
20
25
30
35
0
5
10
15
20
25
30
35
# Tokens per Step
# Tokens per Step
(a) Speed-quality trade-offs of additional parallel decoding methods evaluated on LLaDA 1.5.
(b) Speed-quality trade-off's of additional parallel decoding methods evaluated on Dream 7B.
Figure 19: Speed-qualitg trade-offs of additional parallel decoding methods.
E.2 IMPACT OF FINE-TUNING
We fine-tuned the LLaDA 1.5 model on each task separately. For each task, we generated distinct training and validation sets of 20,000 and 5,000 examples, respectively. The model was trained for 10 epochs using the AdamW optimizer with a batch size of 32, a learning rate of x 10-5, warmup rate of 0.05, and a cosine scheduler. We employed LoRA (Hu et al., 2022) for efficient training, configured with value projection layers, with a dropout rate of 0.05. All experiments were conducted on a single A100 GPU and took approximately 2 hours complete. As detailed in Figs. 20 and 21, fine-tuning improved overall performance but was insufficient to overcome tasks inherently challenging for parallel decoding, such Shuffle, Latin Square, and Inser//eemove/Rellaee Random.
128 and
256, and applied it exclusively to the query, key, and
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110
Accurag 10c
Actursty
R. 2
Acturaty
Acourty
Rinsorigeeet Top-k
Tokons per Stop
Tokons por 9top
Tokens por 9top
TTokons Stop
Toxoms p01 3159
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffic
100
100
Acourayy
Kotuney
Mouuray
61
Tokwen
Tokkens Step
Toxeen Step
TTokwen
Tokwer Shep
(I) Insert Index
(g) Insert Random
(h) Remove Index
(i) Remove Random
(i) Sort
Figure 20: Full Waiting Line (n 3, 4, 5, 6) results using fine-tuned LLaDA 1.5 (Zhu et al., 2025).
Aasunoy
Acsuttyy
Confience Thwahod
Step
(a) Sudoku
(b) Latin Square
Figure 21: Puzzle results using fine-tuned LLaDA 1.5 (Zhu et al., 2025).
E.3 CHAIN-OF-THOUGIIT (COT) PROMPTING
100
Random Top-E
100
100
Let----Rg Right Top-k
< Confidence Top-
Confidence Threshold
80
Aocuracy
Accuracy
Aocuracy
145
16
64
128
145
16
32
64
128
145
16
64
128
Tokens
Step
Tokens per Step
8 Tokens Step
(a) Replace Index
(b) Replace Random
(c) Shuffle
Figure 22: One-shot CoT results Replace Index, Replace Random, and Shuffle. The one-shot examples for each sample are generated by GPT-4.1 Mini (OpenAI, 2025).
To investigate the impact of explicit reasoning on LLaDA 1.5's performance on the Waiting Line tasks, we tested Chain-of- Thought (CoT) prompting. The one-shot examples were generated using OpenAl's 1-Ti----mmi-2025-044 14 API (OpenAI, 2025).
The output token limit was increased from 32 to 256 to accommodate the verbose, multi-step nature of the CoT outputs. Our prompt structured to include the trigger phrase, "Think step step and give your final answer at the end as 'The answer is: {answer) " after the user's question. The full prompt template is shown in Table 4.
As shown in Fig. 22, Chain-of- Thoughh (CoT) improves performance, especially for parallel decod- ing, but at the cost of higher token count.
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Table An example of an one-shot example for Shuffle (CoT) generated with GPT-4.1 Mini (Ope- nAI, 2025).
Question
You are managing waiting line at a customer service desk.
The waiting line should be randomly shuffled to ensure fair service distribution: ["Thomas Holmes", "Keith Ramos", "Victoria Collins", "Roger Hughes", "Austin Dunn"].
Please randomly shuffle the list. Ensure the sequence is different from the original. Think step by step and give your final answer the end as 'The answer is: (answer)'.
Response
Step I: Identify the original list: ['Thomas Holmes", "Keith Ramos", "Victoria Collins". "Roger Hughes", "Austin Dunn"]
Step 2: Randomly shuffle the list ensuring the new sequence is different from the original. One possible shuffled sequence could be: ["Austin Dunn". "Victoria Collins". "Roger Hughes", "Thomas Holmes", "Keith Ramos"]
Step 3: Verify the shuffled list is different from the original: Original first element: "Thomas Holmes" Shuffled first element: "Austin Dunn" They are different, so the shuffle is valid.
The answer is: ['Austin Dunn", "Victoria Collins", "Roger Hughes", "Thomas Holmes", "Keith Ramos"]
RDR
LLaDA-1.5
80
80-
Aourrsy
Accurnay
Acoursay
80
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80-
12
18
12
4
18
12
16
# Tookerss per Step
Tooerrs per Step
TTokerss per Step
(a) Replace Index
(b) Replace Random
(c) Shuffle
Figure 23: RCR (He et al., 2025) results on Replace Index, Replace Random, and Shuffle.
E.4 REMASKING SAMPLERS: RCR AND REMDM
We evaluated two training-free decoding strategies that allow for token revision: Running Confi- dence Remasking (RCR) (He et al., 2025) and Remasking Diffusion Model (ReMDM) (Wang al., 2025), using their official codebases. RCR works by tracking the running maximum confidence for each position over time and continuously remasking tokens that remain uncertain. In contrast, ReMDM performs n revision steps when most of the output is generated, targeting the & tokens with the lowest confidence. For our experiments with ReMDM, we set 1 for simplicity and tested
100
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LLaDA-15 1
80
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Nocurto
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60-
00.
16
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0 Tokenss per Stop
Tolkons por Stop
0 TTokons per Stop
(a) Replace Index
(b) Replace Random
(c) Shuffle
Figure 24: ReMDM (Wang et al., 2025) results Replace Index, Replace Random, and Shuffle.
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various values for n. We found that a single revision step (n 1) achieved optimal performance, with no further improvements observed from additional steps.
In our experiments (Figs. 23 and 24), notice no significant improvements from RCR or ReMDM.
E.5 DISCRETE DIFFUSION WITH UNIFORM TRANSITION MATRIX
This section evaluates two variants of the 90-million-parameter SEDD model (Lou et al., 2024); absorb and uniform. For the absorb variant, we employed the publicly available pre-trained model". For the uniform variant, we pre-trained the model from scratch on the Open Texn dataset (Gokaslan & Cohen, 2019). The pre-training process required 24 hours on eight A100 GPUs.
Subsequently, both variants were fine-tuned on each task. We trained for 32 epochs using the AdamW optimizer with batch size of 64, a learning rate of 3 10-4, and a cosine scheduler with a 0.25 warmup ratio. Each fine-tuning run was conducted on single A100 GPU and completed in approximately one hour.
Absorb
Unioorm
80
80
80
Aoursty
80.5
Accuray
80-
Aouurny
80
145:10
02
54
120
145
10
32
64
128
145
02
64
128
Total deps
Total deeps
Total steps
(a) Replace Index
(b) Replace Random
(c) Shuffle
Figure 25: SEDD (Lou et al., 2024) results on Replace Index, Replace Random, and Shuffle.
F TASK CHARACTERIZATION
F.I CHARACTERIZING TASKS BY PARALLELIZABILITY AND DECODING ORDER
We analyze how the unmasking order and the degree of parallel token decoding influence down- stream scores for each task our benchmark (Fig. 6). We plot the tasks in a scatter plot where the x-axis represents parallelizability and the y-axis represents the benefit from different decoding orders. Tasks on the right are harder to parallelize than those on the left. Tasks on the top benefit from semi-autoregrresivve order, while those the bottom perform better with any-order decod- ing. The results are averaged over the LLaDA 1.5 and Dream 7B models and across four unmasking strategies: Random Top-k, Confidence Top-k, Margin Top-k, and Entropy Top-k.
To define the x-axis (paralleliaabiltty) we evaluate the model with an increasing number of parallel tokens, k. while using full any-order decoding scheme. We then compute metric representing the point at which performance begins to drop. This metric is the center of mass of the scores, calculated Eg (ooee))))))
De score, A smaller value the x-axis therefore indicates that the task is harder to parallelize. We observe that the Shuffle task is the most difficult to parallelize. Seeetene-Seetenee also challenging, as the model must successfully connect words and insert appropriate connecting language while maintaining grammatical correctness. Interestingly, the Latin Square task is harder to parallelize than Sudoku, potentially because multiple valid solutions exist, forcing the model to commit to one solution during generation. Similarly, Insert Random proves harder to parallelize than Insert Index.
To define the y-axis (influence of decoding order), we analyze how semi-autoregressivee decoding affects performance. We fix the number of parallel tokens to h 2 and evaluate the downstream metric for various block lengths. We then fit a line to these scores and use its slope as our met- ric. A positive slope indicates that performance increases as the block length decreases (enforcing
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more autoregressive process), while negative slope indicates that larger blocks fully any-order decoding is preferable. Our results show that most tasks have a negative value, suggesting that the models generally prefer any-order decoding. Text generation tasks, in particular, fall into this cate- gory. We also include four existing benchmarks, GSM8K (Cobbe et al., 2021), HumanEval (Chen al., 2021), IFEval (Zhou et al., 2023), and MATH (Hendryeks et al., 2021) in our analysis. Both tasks appear on the left side of the plot, indicating that models can solve them in a more paral- lel fashion. This finding underlines the need for more challenging benchmarks like the proposed BARALLELBENCE to properly test the capabilities of dLLMs.
Finally, Tables and 6 provide comprehensive taxonomy of the evaluated tasks, characterizing them by their ideal token dependency and the scope of their constraints. As detailed in Table 5, Waiting Line tasks primarily exhibit zero dependency for deterministic tasks, though tasks involving randomness or shuffling introduce global constraints that significantly increase token dependency. In contrast, Table highlights how Text Writing tasks maintain local constraints but scale in dependency from low to very high the difficulty increases. The Puzzles category reflects similar divergence: Sudoku is treated as a deterministic task with zero dependency, while the Latin Square task allows for multiple valid solutions, thereby introducing high dependency.
Table 5: Waiting Line: Dependencies and Constraints.
Category
Waiting Line
Replace Index
Replace Random
Insert Index
Insert Random
Remove Index
Remove Random
Task
Copy
Reverse
Shuffle
Sort
(Ideal) Token
Very High
7ero
7ero
7ero
Medium
Zero
Medium
Zero
Medium
7em
Dependency
Constraint
Type
N/A
N/A
N/A
Global
Global
N/A
Global
N/A
Global
N/A
Table 6: Text Writing and Puzzles: Dependencies and Constraints.
Category
Text Writing
Puzzles
Para- phrasing
Summari- zation
W2S
W2S (Medium)
W22 (Hard)
Latin
Task
Sudoku
(Easy)
Square
(Ideal) Token
Very High
Very High
Low
Low
Medium
High
Zero
Dependency
Constraint
Type
Local
Locul
Local
Local
Local
N/A
Globul
F.2 SPEED-QUALITY TRADE-OFF
Figure illustrates the trade-off between the number of tokens decoded in parallel and the resulting downstream accuracy for each unmasking method. For our experiments, we utilized the LLaDA 1.5 model (Zhu et al., 2025). The accuracy is averaged over all 17 benchmark tasks across the three categories: Waiting Line, Text Writing, and Puzzles.
The oracle performance, marked by a star in the plot, represents an empirical upper bound. To com- pute this, we employ the Confidence Threshold method. For each sample, we identify the minimum threshold (equivalent to the minimum number of total performed steps) that achieves the best possi- ble accuracy. We then average the accuracy and number of steps of these optimal thresholds across all samples and tasks. This simulates hypothetical unmasking strategy that knows in advance the precise minimum effort required to solve each task perfectly.
The results indicate that for Top-k unmasking methods, accuracy degrades rapidly as the number of tokens per step increases. Confidence Threshold, on the other hand, exhibits much more favorable curve, where the drop-off in accuracy occurs at significantly higher number of parallel tokens. Nevertheless, substantial gap remains when compared to the oracle. While all methods perform comparably when unmasking single token per step, the oracle maintains high accuracy at a far greater decoding parallelism. This suggests that, in theory, unmasking could be performed much faster without sacrificing accuracy if a more effective sampling method were available.
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F.3 SPEED-QUALITY OFF IN EXISTING BENCHMARKS
In this section, we assess the behaviour of parallel decoding on tasks not specifically designed for benchmarking parallel decoding performance, reporting speed-quality trade-off's Fig. 26 shows the results for GSM8K (Cobbe et al., 2021), IFEval (Zhou et al., 2023), and MATH (Hendrycks et al., 2021), using LLaDA 1.5 with varying degrees of parallelism. All benchmarks exhibit a similar trend of decreasing accuracy as the number of tokens per step increases. Even when decoding one token per step, these benchmarks already exhibit substantial difficulty, which implies that model capacity remains a dominant factor that cannot be separated from the analysis. In contrast to our benchmark tasks, all existing tasks show slight accuracy degradation as parallelism increases. Due to these two properties, existing benchmarks do not permit clear evaluation of whether parallel decoding method can effectively control or adapt its level of parallelism in relation to task difficulty.
100
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Letro dight Top Derbleee Themsook
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Tohens Step
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(a) Speed quality trade-off's on (b) Speed-quality trade-off's
(c) Specd-quality trade-offs on
GSM8K using LLaDA 1.5.
IFEval using LLaDA 1.5.
MATH using LLaDA 1.5.
Figure 26: Speed-quality trade-offs of existing benchmarks.
F.4 TIME-QUALITY TRADE-OFF
We provide actual wall-clock latency measurements and their corresponding time-quality curves in Fig. 27. We obtained these results using a single A100 80GB GPU with a batch size of 1.
Notably, the time-quality curve mirrors the speed-quality curve shown in Fig. 7 (where the x-axis represents tokens per step). This indicates that analyzing the trade-off using tokens per step rather than bardwarr-dependentt latency measurements is sufficient and reliable.
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ght Confidennon Totee Confidonce Threstalc Orodic
0.8 Latency (8)
1.0
1.2
Figure 27: Time-quality trade-off.
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G
FAILURE CASES
We present several failure cases observed when using LLaDA 1.3 (Zhu et al., 2025) with Confidence Top-k (k: 2). These examples highlight specific weaknesses inherent to parallel decoding.
Incorrect Swapping of Names Waiting Line (Shuffte)
Input: ["Jack Burns", "Jessica Martin", "Tyler Lopez"]
Model Output: ["Jessica Lopez", "Jack Burns", "Tyler Martin"]
Analysis: The model incorrectly swaps the first and last names of two persons. This flaw highlights the risk of the conditional independence assumption dLLMs.
Word Repetition in Summarization
Input: "Summarize the following conversation. [...] Daniel: Cool."
Model Output: "Missy gets out of work at pm and she drinks drinks after dinner."
Analysis: The model incorrectly repeats the word "drinks." This is a common artifact in parallel decoding, where the lack of one-by-one conditioning cause the model to generate the same token in adjacent positions.
Grammatical Error in Paraphrasing
Input: "Paraphrase the sentence: 'How do deal with a rude student?"
Model Output:
"What strategies can use handle disrespectful student?"
Analysis:
The output contains a grammatical error in "an disrespectful". This demonstrates that the model fails enforce local syntactic rules, as the choice of article depends on the subsequent token, a dependency that is weakened in parallel generation scheme.
Grammatical Error in Words-to-Sentence
Input: "Construct single, coherent sentence using the words ball, bridge, elephant, and open."
Model Output: "The elephant walked across the the old bridge, looking carrying an open ball."
Analysis:
The generated sentence is syntactically flawed, due to both a duplicated article ("the the") and wrong verb sequence ("looking carrying"). This failure to form coherent clause underscores the difficulty parallel decoding has in maintaining long-range grammatical structure.
H COMPREHENSIVE EXPERIMENTAL RESULTS
H.1 COMPARISON WITH LARGE LANGUAGE MODELS
Tables 7 to 9 present a performance comparison between open-source dLLMs, a closed-source dLLM Mercury (Inception Labs al., 2025), and several popular autoregressive LLMs, including Qwen (Yang et al., 2024; 2025a), Llama (Grattafiori et al., 2024), and Claude Haiku 3.5 (Anthropic, 2024). To create more challenging benchmark for this comparison, we increased the list length of the Waiting Line task to 15 with 128 output tokens. For the open-source dLLMMs, we set the number of tokens decoded parallel k and did not use semi-auttregressive decoding. In contrast, we had control over Mercury's parallel decoding settings, which we assume handled internally.
The results indicate that even commercial model like Mercury cannot achieve perfect score on Shuffle, yet it successfully solves Reverse with 100% accuracy. Furthermore, the relatively simple task of producing a Latin Square proved rather challenging for Mercury, whereas it was casier for most LLMs that decode tokens one by one. Nevertheless, Mercury exceeds or matches the perfor- mance of open-source models most tasks.
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Table Benchmark results for Waiting Line.
Waiting Line
Mode/ Dataset
Copy
Scrt
Ind.
Rep.
Rep.
LIaDA (Nis et al., 2025)
100.0
0.0
97.0
21.0
14.0
85.0
18.0
82.0
15.0
58.0
LLaDA (2hu al., 2025)
100.0
0.0
99.0
18.0
14.0
86.0
21.0
77.0
15.0
70.0
al.,
DiffuCodrr (Gong et al., 2025)
58.0
0.0
28.0
32.0
51.0
10.0
35.0
19.0
57.0
Mercury (Inception Labs et al., 2025)
100.0
0.0
100.0
92.0
63.9
95.0
15.0
90.0
28.0
98.0
Owen2.5 (Yang al., 2024)
100.0
0.0
10.0
39.0
96.0
19.0
72.0
19.0
53.0
Owen2.5 (Yang
2024)
Owen3 48 (Yang et al., 2025a)
100.0
0.0
75.0
97.0
77.9
89.0
43.0
47.0
67.0
92.0
Lama 3.1 8B (Grattafioci al., 2024)
100.0
64.0
100.0
96.0
50.0
93.0
22.0
63.0
23.0
$8.0
(Gritaalios
303
(Anthropic, 2024)
5.0
100.0
Table 8: Benchmmrk results for Text Writing.
Text Writing
Model/ Dutaset
Paruphrasing
Summarization
W2S (casy)
WIS (medium)
W25 (hard)
Grammar
BERT
[-BL EU
Grummur
ROUGE-L
Grammar
Acc.
Grammur
Acc.
Gmmmur
Acc.
LLaDA (Nie 2025)
95.2
82.1
85.0
43.2
2025)
Droum 7B (Ye al., 20256]
91.0
93.5
32.5
85.0
40.3
61.0
K3.0
DiffaCoder (Gong et al., 2025)
$6.0
94.2
54.7
78.0
41.9
87.0
53.0
87.0
72.0
13.0
50.0
Mercwyy (Inception Labs al. 2025)
98.0
95.2
84.4
93.0
31.1
99.0
50.0
100.0
94.0
99.0
$4.0
Qwen2.5 3B (Ying 2024)
100.0
94.7
84,8
95.0
38.2
99.0
54.0
99.0
80.0
96.0
73.0
Qwen2.5 7B (Yang
2025a)
Lhaa 3.1 (Grataalioni al., 2024)
99.0
93.3
92.0
39.4
97.0
92.0
96.0
98.0
99.0
Llana 1.2 38 (Grsttaffooi ol., 2014)
99.0
92.9
88.8
97.0
36.4
98.0
75.0
96.0
94.1
99.11
70.0
Clande Haiku 3.5 (Anthroii, 2024)
99.0
92.3
96.2
99.0
34,3
100.0
93.0
98.0
97.0
99.0
84.0
Table Benchmark results for Puzzle.
Puzzle
Model Dataset
Sudoku
Latin Square
L.LADA (Nie et al., 2025)
14.8
36.0
2025)
Dream (Yo al, 2025b)
95.4
34.7
DiffuCoder (Gong et al. 2025)
16.7
10.0
(laception Labs 2025)
59.0
Owen2.5 (Yang al., 2024)
2.8
16.0
Qwen2.5 7B (Yang al., 2024)
1.9
88.0
Qwen3 (Yang
2025e)
Lluma 3.1 (Gratiafioni et al., 2024)
0.0
24.0
Llama 3.2 3B (Grattation et al., 2024)
0.0
12.0
Claude Haiko [Anhhropic, 2024)
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H.2 COMPLETE BENCHMARK RESULTS
Bar den Tipe
Our leenc "wesfodd
Shep
Sho
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffle
depp
Blace Shop
(f) Insert Index
( Insert Random
(h) Remove Index
(i) Remove Random
(j) Sort
Shop
dep
Taoos Shop
(k) Paraphrasing
Summarization
(m) W2S (easy)
(n) W2S (medium)
(0) W2S (hard)
Tenemu per Stop
Tosemm Skop
(p) Sudoku
(q) Latin Square
Figure 28: Full PARALLELBENCH results using LLaDA 1.0 (Nie et al., 2025).
I AUTOREGRESSIVE LLM PARALLEL DECODING
In this section, we demonstrate that PARALLELBENCE BENCH generalizes beyond Diffusion LLMs to other parallel decoding paradigms. We examine Medusa (Cai et al., 2024), speculative decoding frame- work that augments the frozen backbone of an autoregressive LLM with multiple lightweight decod- ing heads. Instead of relying on separate draft model. these heads simultancously predict multiple future tokens based on the current step's hidden states. Candidates are then organized into tree structure and verified in single parallel forward pass using Tree Attention, accepting the longest valid prefix.
To analyze the accuracy of parallel predictions across varying difficulty levels, we modify the Medusa inference process. Rather than utilizing the dynamic verification mechanism, we force the model to decode a fixed number of tokens per step (ranging from to 5). We employ Vicuna- 1.5-7B (Chiang al., 2023) as the backbone.
Fig. 33 illustrates the performance across benchmark tasks. We observe a significant drop in quality when increasing the number of parallel tokens from 1 to 2, affecting even simple tasks like Copy. Furthermore, complex tasks such as Puzzles generally exhibit very low performance. These re- sults confirm that PARALLELBENT BENCH effectively evaluates arbitrary parallel decoding architectures, highlighting the challenges of parallelization even in autoregressive LLM settings.
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Accuracy
Aosurcy
Farcznn Righ-To-- Oorkdence hand
Shpp
Tokams
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffic
Aocuocy
Aocuracy
Nouurry
Tockers
Insert Index
(g) Insert Random
Remove Index
Remove Random
(i) Sort
Accurdy
(k) Paraphrasing
Summarization
(m) W2S (easy)
(n) W2S (medium)
(a) W2S (hard)
Acsunsy
Aucunay
8 8
Step
(p) Sudoku
(q) Latin Square
Figure 29: Full BARALLELBENCH results using LLaDA 1.5 (Zhu et al., 2025).
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Raraan San Tape
24
Shop
Stap
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffic
Stap
Insert Index
( Insert Random
Remove Index
Remove Random
(j) Sort
Stop
Sep
(k) Paraphrasing
Summarization
(m) W2S (easy)
(n) W2S (medium)
(a) W2S (hard)
(p) Sudoku
(q) Latin Square
Figure 30: Full PARALLEL ENCH results using Dream 7B (Ye et al., 2025b).
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Rar San Tape Oo Kraae Theshhod
24
Shap
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(c) Shuffic
12
Stop
Stap
Takans
Insert Index
(g) Insert Random
Remove Index
Remove Random
(j) Sort
Stop
depp
Seop
(k) Paraphrasing
Summarization
(m) W2S (easy)
(n) W2S (medium)
(a) W2S (hard)
(p) Sudoku
(q) Latin Square
Figure 31: Full PARALLELBENCH results using DiffuCoder (Gong et al., 2025).
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130
(a) Copy
(b) Reverse
(c) Replace Index
(d) Replace Random
(e) Shuffle
(I) Insert Index
(g) Insert Random
(h) Remove Index
(i) Remove Random
ii Sort
va
124
(k) Paraphrasing
(l) Summarization
(m) W2S (easy)
(n) W2S (medium)
(0) W2S (hard)
100
(p) Sudoku
(q) Latin Square
Figure 32: Full PARALLEI. results using LLaDA 1.5 (Zhu al., 2025) with PrefixCache (Wu et al., 2025).
Modee
Accurccy
Nosurscy
Step
per Swpp
Stop
Sxp
Copy
Reverse
(c) Replace Index
(d) Replace Random
Shuffle
10c
Accuracy
Aocuray
Tokent Step
Tokken per Step
Tokeet per Step
Tokken Shep
Tokeee per Step
( Paraphrasing
W2S (easy)
(h) W2S (hard)
(i) Sudoku
(i) Latin Square
Figure 33: Benchmark results of Medusa (Cai et al., 2024) on RRAALELLBENCH Waiting Line (Figs. 33a 33e), Text Writing (Figs. 33f to 33h), and Puzzles (Figs. 33i and 33j).
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LLM USAGE DISCLOSURE
We utilized Gemini 2.5 Pro (Google Deepmind, 2025) and GPT-4.1 Mini (OpenAI, 2025) to generate our benchmark dataset. Additionally, Gemini 2.5 Pro was used assist with improving the gram- mar, clarity, and readability of this manuscript. The authors reviewed and edited all LLM-generated content and suggestions to ensure the final text accurately reflects our scientific contributions and claims. The authors retain full responsibility for the content of this paper.
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Reviews:
[{"review_id": "CiDFtfl4we", "reviewer": "Reviewer_WAQL", "summary": "The paper studies parallel decoding in diffusion-based large language models (dLLMs) in order to address the challenge that parallel decoding often fails to capture inter-token dependencies leading to quality degradation, due to the conditional independence assumption among tokens.\n\nThe authors make three main contributions:\n\t\n1. Information-theoretic analysis — They formalize the lower bound of parallel decoding quality loss using conditional total correlation C(Y|X), proving that even ideal models face an inherent speed–quality trade-off.\n\t\n2.\tSynthetic case studies — They analyze list operations like Copy, Replace Random, and Shuffle to quantify how dependency strength affects parallel decoding accuracy.\n\t\n3.\tPARALLELBENCH — A new benchmark with 17 tasks across 3 categories (Waiting Line, Text Writing, Puzzles) to empirically evaluate dLLMs and AR LLMs. It exposes how parallel decoding degrades quality in realistic settings and shows that current adaptive unmasking methods (e.g., Top-k, Threshold) cannot fully balance speed and accuracy.\n\nThe paper concludes that dLLMs suffer from severe quality degradation under parallel decoding, especially in dependency-heavy tasks, and that current decoding strategies fail to adapt parallelism dynamically to task difficulty.", "questions": "1. The oracle analysis suggests per-sample thresholds could yield large gains — how feasible is this in practical inference (e.g., latency, calibration)?\n\n2. How do results change with larger blocks or variable block scheduling strategies beyond fixed lengths (with semi-AR)?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The use of conditional total correlation to quantify unavoidable quality loss provides a solid mathematical basis for analyzing the parallel decoding trade-off, making the paper has clear theoretical grounding.\n\n2. The combination of theoretical proofs, synthetic tasks, and realistic benchmarks (including grammar-sensitive and reasoning tasks) provides a well-rounded evaluation.\n\n3. The combination of theoretical proofs, synthetic tasks, and realistic benchmarks (including grammar-sensitive and reasoning tasks) provides a well-rounded evaluation.\n\n4. The writing, presentations accompanied with interpretations are overall clear. Code is publicly released, and the benchmark tasks are well-documented, facilitating future research.", "weaknesses": "1. Although 17 tasks span diverse categories, most involve short outputs or synthetic patterns; results may not generalize to long-context reasoning or dialogue generation.\n\n2. Comparisons largely focus on fixed unmasking or basic threshold schemes, missing newer adaptive scheduling approaches (e.g., dilated scheduling, SlowFast decoding, or hybrid AR-diffusion). \n\n3. The paper focuses on decoding strategies, not how model pre-training or architecture might affect the issue. \n\n4. Other decoding/scheduling work that should be covered (and possibly compared): the paper could be strenghthen to include decoding strategies that cover dynamic stage-based scheduling [1], dilated unmasking[2], block decoding [3,5] and revocation/remasking [4]. \n\n\n\n-----\nReferences\n1. Accelerating Diffusion Large Language Models with SlowFast Sampling: The Three Golden Principles (Wei et al., 2025) \n2. Plan for Speed: Dilated Scheduling for Masked Diffusion Language Models (Luxembourg, Permuter, Nachmani, 2025) \n3. Fast‑dLLM: Training‑free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding \n4. Wide‑In, Narrow‑Out: Revokable Decoding for Efficient and Effective DLLMs (Hong et al., 2025)\n5., Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models (Arriola et al., 2025)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "8IHwVfLBvZ", "reviewer": "Reviewer_uEfF", "summary": "his paper investigates the speed–quality trade-off in parallel decoding for Diffusion Language Models (dLLMs). Although dLLMs promise faster inference through parallel decoding, the underlying conditional independence assumption often leads to severe quality degradation in tasks with strong token dependencies. To expose this issue, the authors provide an information-theoretic analysis and introduce ParallelBench, specifically designed for evaluating dLLMs under parallel decoding. It comprises 17 tasks across three categories (Waiting Line, Text Writing, Puzzles) that are easy for humans and autoregressive (AR) models but challenging for dLLMs. Experiments reveal that (1) dLLMs experience substantial quality loss during parallel decoding, and (2) existing decoding strategies (both static and adaptive) fail to balance quality and speed effectively.", "questions": "See Weaknesses", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper tackles a core dLLM challenge: the quality impact of parallel decoding, a key advantage over AR models, and highlights the limitations of existing benchmarks in assessing it.\n2. Provides theoretical insights.\n3. Clearly illustrates token dependency variations across tasks through analysis of synthetic “list operations” such as Copy, Replace Index, Replace Random, and Shuffle.\n4. Systematically evaluates multiple dLLMs—including LLaDA, Dream, and the closed-source Mercury—across various decoding strategies such as Top-k, Threshold, and Semi-AR on PARALLELBENCH.", "weaknesses": "1. Need for benchmark comparison: More experiments are needed to show PARALLELBENCH’s added value over existing benchmarks.\n2. Missing actual speed measurements: Experiments focus on parallelism vs. quality, but no wall-clock latency or time–quality curves are provided.\n3. Limited real-world coverage: The benchmark may not capture all challenges dLLMs face in complex, open-ended tasks.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "UH9IhDLGJ0", "reviewer": "Reviewer_o6Fd", "summary": "The paper introduces ParallelBench, a benchmark and analysis suite for diffusion LLMs (dLLMs) that isolates the speed--quality trade-offs of parallel decoding. It provides an information-theoretic lower bound (via conditional total correlation) showing why parallel decoding degrades when token dependencies are strong, confirms the theory on analytically tractable list operations, and then demonstrates the same failure modes on realistic tasks across three categories (Waiting Line, Text Writing, Puzzles). The study further contrasts static (Top-k) and adaptive (Threshold) unmasking, semi-AR strategies, and \"oracle\" per-sample thresholds, revealing substantial headroom for adaptive methods.", "questions": "1. You show big gaps between fixed thresholds and the oracle per-sample threshold. How close can a simple learned heuristic (say, a tiny classifier on token stats) get to the oracle without heavy training?\n\n2. The task taxonomy is useful. Could you add a small table of \"meta-features\" (rough dependency strength, locality vs. global constraints, etc.) so practitioners can guess which decoding policy to use before running heavy tests?\n\n3. Semi-AR helps sometimes and hurts other times. Do you envision a lightweight runtime policy that flips block sizes per sample using quick signals (entropy, margin, \"AR-ness\")? Any early results there?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The theory connects nicely to practice: the conditional-correlation argument predicts the “New City” style errors you later see in real tasks. It’s satisfying when the math lines up with the plots.\n\n2. The benchmark fills a gap. We've all seen parallel decoding look great in one demo and fall apart in another; this suite finally gives a way to measure where it cracks and by how much.\n\n3. The oracle threshold curves are especially helpful -- they show there’s real headroom for adaptive, per-sample control rather than one-size-fits-all knobs.\n\n4. The write-up is clear and the figures are readable; I didn’t have to reverse-engineer the setup to follow the argument.", "weaknesses": "1. Coverage feels a bit narrow in the main text. A compact table that pulls model/method results out of the appendix would make the big picture easier to scan.\n\n2. The quality metrics are fine, but a couple more \"at a glance\" indicators (e.g., BERTScore or constraint-violation counts) would help interpret how quality degrades as parallelism goes up.\n\n3. Most examples are short sequences. One longer-form scenario in the main paper would help readers judge whether the conclusions hold in more realistic lengths.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "vrqZiyjVQC", "reviewer": "Reviewer_vHaA", "summary": "The paper presented an information-theoretic analysis on the capabilities of diffusion LLMs using toy tasks to compute their theoretic bounds. The paper performed a distribution based analysis and a decoding strategy based analysis. The paper also presented ParallelBench, composed of the toy tasks and realistic tasks, to evaluate the capabilities of dllms empirically.", "questions": "- How is it that Sudoku having supposedly C(Y|X) = 0 and Latin Square having C(Y|X) > 0, but the empirical results showing that LLaDA 1.5 performs better on Latin square than Sudoku? \n- On Figure 7, what is the arrow indicative of?\n- Is there a reason why ParallelBench is for evaluating dLLM specifically and not parallel decoding in different LLMS (e.g. parallel decoding in AR LLMs) in general?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The paper presents a theoretical explanation for the capabilities and limitations of parallel decoding with dLLMs. This provides some intuition for whether to use dLLMs or whether to enable decoding multiple tokens per step depending on the task at hand. The theoretical result is corroborated with empirical results on the same toy tasks.\n- The empirical evaluation performed a wide variety of ablations that provide some insights on how different unmasking techniques and models compare.\n- The presented benchmark can serve as a baseline for evaluating whether a particular language model/decoding technique can adaptively exploit parallelism, beyond dLLMs.", "weaknesses": "- The empirical evaluation on realistic tasks seem to deviate from the expectations set by the theoretical results. For example LLaDA 1.5 performs better on Latin Square than Sudoku, but Sudoku has C(Y|X) = 0 while Latin Square has C(Y|X) > 0. This weakens the significance of the theoretic analysis. The difference in complexity from the toy tasks to realistic tasks seem dominate the difference in task type.\n- The empirical results for 3f-j show accuracy going down as the # tokens per step increase, which is to be expected that the more naive parallelism (as in the technique does not explicitly target/decide when parallelism is appropriate) employed the worse the accuracy would be. Most realistic tasks should fall into these regimes, rather than the extremes of Copy or Replace Index. And it is unlikely to be possible to perform the same information-theoretic analysis on realistic tasks to quantify the theoretic accuracy. \n- The best the analysis provides is an intuition, which in general can be useful. However, the intuition that more dependencies between tokens in the expected response makes parallelism harder is hardly surprising. The difficult task is knowing when parallelism can be enabled, which the work does not provide directions towards any solutions, as the toy examples shown do not generalize/scale to real examples.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)