Beyond Scattered Acceptance: Fast and Coherent Inference for DLMs via Longest Stable Prefixes
Authors: Pengxiang Li
Jiayin Cai
Hongwei Xue
Kunyu Shi
Shilin Yan
Venue: ICLR 2026 Poster (2026)
Keywords: diffusion language model
efficent
block
Primary area: generative models

Abstract: Diffusion Language Models (DLMs) promise highly parallel text generation, yet their practical inference speed is often bottlenecked by suboptimal decoding schedulers. Standard approaches rely on ``scattered acceptance''---committing high-confidence tokens at disjoint positions throughout the sequence. This approach inadvertently fractures the Key-Value (KV) cache, destroys memory locality, and forces the model into costly, repeated repairs across unstable token boundaries. To resolve this, we present the \textbf{Longest Stable Prefix (LSP)} scheduler, a training-free and model-agnostic inference paradigm based on \textit{monolithic prefix absorption}. In each denoising step, LSP evaluates token stability via a single forward pass, dynamically identifies a contiguous left-aligned block of stable predictions, and snaps its boundary to natural linguistic or structural delimiters before an atomic commitment. This prefix-first topology yields dual benefits: systemically, it converts fragmented KV cache updates into efficient, contiguous appends; algorithmically, it preserves bidirectional lookahead over a geometrically shrinking active suffix, drastically reducing token flip rates and denoiser calls. Extensive evaluations on LLaDA-8B and Dream-7B demonstrate that LSP accelerates inference by up to 3.4$\times$ across rigorous benchmarks---including mathematical reasoning, code generation, multilingual (CJK) tasks, and creative writing---while matching or slightly improving output quality. By fundamentally restructuring the commitment topology, LSP bridges the gap between the theoretical parallelism of DLMs and practical hardware efficiency.

Published as a conference paper at ICLR 2026
BEYOND SCATTERED ACCEPTANCE: FAST AND Co- HERENT INFERENCE FOR DLMS VIA LONGEST STA- BLE PREFIXES
Pengxiang Li
Joey Tsai
Hongwei Xue
Kunyu Shi
Shilin Yan
1 Accio Team, Alibaba Group
TTinggua University
Project Leader
Corresponding Author
ABSTRACT
Diffusion Language Models (DLMs) promise highly parallel text generation, yet their practical inference speed is often bottlenecked by suboptimal decod- ing schedulers. Standard approaches rely on "scattered acceptance" commitiing commingc"" high-confidence tokens disjoint positions throughout the sequence. This ap- proach inadvertently fractures the Key-Valus (KV) cache, destroys memory lo- cality, and forces the model into costly, repeated repairs across unstable token boundaries. To resolve this, we present the Longest Stable Prefix (LSP) sched- uler, training-free and model-agnostic inference paradigm based on monolithic prefix absorption. In each denoising step. LSP evaluates token stability via single forward pass, dynamically identifies a contiguous left-aligned block of stable pre- dictions, and snaps its boundary natural linguistic structural delimiters before an atomic commitment. This prefix-fire first topology yields dual benefits: systemi- cally, it converts fragmented KV cache updates into efficient, contiguous appends; algorithmically. it preserves bidirectional lookahead over geometrically shrink- ing active suffix, drastically reducing token flip rates and denoiser calls. Exten- sive evaluations on LLaDA-8B and Dream-78 7B demonstrate that LSP accelerates inference by up 3.4x across rigorous senchmarks-inclluee reasoning, code generation, multilingual (CJK) tasks, and creative writing-while while matching or slightly improving output quality. By fundamentally restructuring the commitment topology, LSP bridges the gap between the theoretical parallelism of DLMs and practical hardware efficiency.
mathematical
INTRODUCTION
Diffusion Language Models (DLMs) have emerged as compelling alternative autoregressive generation, offering an intrinsically parallel inference process that leverages bidirectional con- text (Austin et al., 2021a). This paradigm holds the promise of significant latency reductions traditional one-token-at-a-timee decoding. However, this promise remains largely unfulfilled in prac- tice. The iterative refinement process, central DLM generation, is frequently bottlenecked not by the model's architecture, but by the strategy used to commit intermediate predictions. This creates stark paradox: models designed for parallelism are often constrained by the sequential nature of their own convergence.
At the heart of this inefficiency lies the prevalent strategy of scattered acceptance, where tokens are committed independently based on local confidence (Nie et al., 2025) or in fixed-size, semi- autoregressive blocks (Arriola et al., 2025). This approach fundamentally costly in two distinct ways. First, from an algorithmic perspective, it creates a fragmented sequence of frozen and mu- table tokens. The numerous boundaries between these regions are unstable, requiring repeated, localized repairs that slow the convergence to globally coherent output. Second, from sys- tems perspective, this fragmentation shatters the Key-Value (KV) cache into small, non-contiguous segments, destroying the memory locality that is critical for efficient Transformer inference. Conse- quently, the active (uncommited) portion of the sequence remains long, keeping attention compu- tationally expensive for many iterations.

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Published as a conference paper at ICLR 2026
In this work, we argue that overcoming this bottleneck requires commitment topology. We introduce the Longest Stable Prefix (LSP), a training-free, model-agnostic scheduling paradigm founded the principle of monolithic prefix absorption. Instead of accepting scattered islands of confident tokens, LSP identifies and commits the longest contiguous, stable prefix of the remain- ing active sequence in single atomic step. This is achieved through lightweight, single-pass procedure: (1) it computes a logit margin score for each active position; (2) it adaptively selects margin threshold target a fractional block size (e.g., 25-50% of the active suffix); and (3) snaps the candidate block's 's boundary to a nearby structural delimiter (e.g., punctuation or newline) be- fore committing. A simple fallback rule guarantees progress by committing least one token per iteration, even when the model is highly uncertain.
This prefix-first geometry fundamentally alters the computational dynamics of DI.M inference. By design, the frozen prefix grows as single, contiguous block. This maximizes KV cache reuse and ensures subsequent attention queries are focused on a rapidly shrinking active suffix. The adaptive thresholding strategy encourages the active sequence length to decay geometrically, leading to near-quadratic total work complexity that scales gracefully with sequence length. Algorithmically, committing structurally-alige alligned monolithic blocks minimizes the cross- tross-boundary conflicts inherent in scattered acceptance, reducing the number of repair cycles needed to achieve a coherent state.
Our contributions are threefold:
We identify scattered acceptance as primary bottleneck in DLM inference and propose monolithic prefix absorption as more efficient commitment topology. We instantiate this principle in LSP, a novel, training-fres scheduler that uses a single forward pass, adaptive thresholding, and structural snapping to commit the longest stable prefix.
We provide a computational analysis showing how LSP's prefix- first strategy synergizes with KV caching to induce a geometric decay the active sequence length, focusing com- putation on a shrinking suffix and yielding near-quadratic total work.
Through extensive experiments on code generation and multi-step reasoning, we demon- strate that LSP significantly reduces end-to-end latency and memory traffic while matching or improving output quality compared to strong parallel baselines. Ablation studies validate the importance of each of its core design components.
2 RELATED WORK
2.1 DIFFUSION LARGE LANGUAGE MODEL
Early attempts to transplant diffusion ideas into discrete domains date back to Sohl-Dickstein et al. (2015) and Hoogeboom al. (2021). Building on these foundations, D3PM (Austin et al., 2021a) introduced a unifying probabilistic view in which a discrete-state Markov forward process progressively corrupts clean sequences and parameterized reverse model is trained via ELBO objective to reconstruct text from noisy inputs. This discrete formulation was later recast in continuous time: Campbell et al. (2022) modeled the corruption dynamics as continuous-time Markov chain (CTMC). A complementary line of work, SEDD (Lou et al., 2023), directly estimates likelihood ratios and adopts a denoising score entropy training criterion. Recent analyses MDLM (Shi et al., 2024; Sahoo et al., 2024; Zheng et al., 2024) and RADD (Ou et al., 2024)-244 forr-)-fur- ther reveal that multiple parameterizations of masked/discrete diffusion models are mathematically equivalent, clarifying relationships among prior formulations.
Motivated by these advances, practitioners have scaled diffusion-styye language models into real systems. Commercial offerings include Mercury (Labs et al., 2025), Gemini Diffusion (DeepMind, 2025), and Seed Diffusion (Song et al., 2025b), while LLaDA (Nie et al., 2025) and Dream (Ye et al., 2025) exemplify open-source counterparts. Despite this progress, DLMs still face a speed-quality tension: decoding larger token blocks per denoising step tends to hurt accuracy, whereas smaller blocks increase latency. Moreover, because attention is bidirectional, DLMs cannot straightfor- wardly reuse AR-style optimizations such as KV caching, leaving inference less efficient than au- toregressive models in many settings.
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2.2 ACCELERATION METHODS FOR DIFFUSION LANGUAGE MODELS
Efforts to accelerate DLM inference while preserving quality broadly fall into three complemen- tary tracks. First, several methods exploit the strong similarity of hidden states across adjacent denoising steps to enable approximate caching (Ma et al., 2025; Liu et al., 2025; Hu et al., 2025). closely related strategy restructures generation into semi-/block-autooegresss past blocks (or contexts) can be cached and selectively refreshed during decoding (Wu et al., 2025; Arriola et al., 2025; Song et al., 2025a). Second, token- pakknng approaches reduce attention cost by removing positions deemed less useful; DPad (Chen et al., 2025), for instance, treats distant suf- fix tokens as a temporary scratchpad and prunes them before computation. Third, sampling-focusee techniques aim either to increase the number of tokens accepted per step to cut the total number of soops-sometimes via reinforcement learning (Song et al., 2025b). Within this vein, the number of simultaneously decoded tokens can be governed by confidence/entropy criteria, adjusted online with denoising dynamics (Wei et al., 2025; Huang & Tang, 2025), aligned with small auxiliary AR mod- els (Israel al., 2025), paired with speculative decoding that drafts using the DLM itself (Agrawal et al., 2025).
schedules so that
Our work departs from these optimization routes by capitalizing on an empirical property of DLMs: the correct final answer often appears at intermediate steps. We leverage this early answer con- vergence perform training-free early commitments that reduce computation without sacrificing quality. Concurrently, MidTrruth WWang et al., 2025) also identifies early convergence but pursues temporal ensembling across steps boost accuracy, whereas we develop an early-commit decoding scheme that shortens inference while maintaining performance.
3
METHOD
In this section, we detail our proposed approach for accelerating Diffusion Language Model (DLM) inference. We begin by formalizing the standard discrete diffusion framework and pinpointing the inherent inefficiencies of conventional scheduling strategies. We then introduce the Longest Stable Prefix (LSP) scheduler, a training-free, model-agnostic paradigm designed to overcome these limi- tations. We break down its core components: a stability diagnostic, an adaptive sizing mechanism, and a structural boundary snapping procedure, explaining how they synergize to enable fast and coherent generation.
3.1 PRELIMINARY
Our work is situated within the established framework of discrete diffusion models for language, which have demonstrated remarkable scalability and generation quality (Austin et al., 2021a; Nie et al., 2025). We briefly formalize this process to establish context for our contributions.
Forward Corruption Process. The process begins with a clean text sequence xo = (x at) of length L. sampled from the data distribution Pdata A forward Markov process gradually corrupts this sequence over a series of discrete timesteps f E {1..... T}. At each step t, a subset of tokens in the sequence x;-1 is replaced by special '[MASK]' token produce a noisier sequence x,- The transition probability, (x, -x) is designed such that the degree of masking increases mono- tonically with f. By the final step, the sequence Xy is composed entirely of '[MASK]' tokens. A key property of this process is that the state at any intermediate step can be sampled directly from the original sequence via g(x:|xo) which models the probability that each token in Xo has been absorbed into the "[MASK] state after steps. This property is crucial for formulating tractable training objective.
Reverse Generation Process. The goal of DLM, parameterized by 0, is to learn the reverse of this corruption process. Given a noisy sequence x,, the model is trained to predict the original clean sequence Xa by optimizing a loss function based on the negative likeliood of the ground-truth tokens, thereby learning the conditional distribution po (Xo Xx).
Sequence generation, or sampling, is an iterative procedure that inverts the forward process, starting from a fully masked sequence Xy. For each timestep t from T down to 1, two-stage refinement is performed. First, in prediction step, the model po is called to predict the entire clean sequence
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10.2, 0.8, 0.4, 0.6, 0.3, 0.9, 0.7]
t=
Prompt
[M]
[M]
[M]
[M]
[M]
[
[
[
0.6
commit tokens
[0.7, 0.8, 0.2, 0.6
t-
Prompt
The
quick
brown
[M]
[M]
[M]
[M]
[M]
0.6
commit 3 tokens
8 [0.9, 0.8]
t=2
Prompt
The
quick
brown
jumps
over
[M]
[M]
commit
Final
Prompt
The quick brown jumps the lazy
Complete o
Margin
Token
Frozen prefix
M
Active suffix
Figure The iterative process of the Longest Stable Prefix (LSP) scheduler. In each step, LSP performs a single forward pass to assess the stability of predictions for the current active suffix, measured by the logit margin (6;). Instead accepting scattered tokens, it atomically commits the longest contiguous prefix of tokens that meet an adaptively determined stability threshold (r). As shown, the frozen prefix (green) grows monolithically, causing the active suffix (white) shrink.
from the current noisy state: &n ~ (- Second, re-masking step, new, less noisy state X,-1 is constructed by combining information from the current state x, and the prediction &o-
The Inefficiency of Conventional Schedulers. The critical decision in the re-masking step lies with the scheduling strategy, which determines which tokens from the prediction Xo are accepted (or "committed") and which positions are re-masked for further refinement. Most cxisting schedulers operate principle of scattered acceptance: they identify and commit tokens independently based on local confidence scores (e.g.. high probability or low entropy). This approach, while intuitive, introduces profound inefficiencies. Algorithmically, it creates fragmented sequence of frozen (committed) and active (mutable) tokens. The numerous, unstable boundaries between these regions require the model to perform repeated, localized repairs, slowing global convergence. Systemically, this fragmentation shatters the Key-Vatt Value (KV) cache into small, non-contiguous segments. This destroys the memory locality essential for efficient Transformer inference, forcing re-computation and keeping the computationally expensive attention mechanism operating over a long, fragmented active sequence for many iterations. This fundamental bottleneck motivates new commitment topology.
3.2 THE LONGEST STABLE PREFIX (LSP) SCHEDULER
To address the aforementioned bottleneck, we introduce the Longest Stable Prefix (LSP) scheduler. disciplined strategy of monolithic prefix absorption. Instead of accepting scattered islands of confident tokens, LSP's core principle is to identify and commit the longest possible contiguous and stable block from the left of the active sequence in single, atomic operation. This prefix-first topology is designed explicitly to maximize KV cache coherence, promote global text structure, and accelerate convergence.
At any generation iteration k. we partition the full sequence into two parts: frozen prefix x=()) which is cached and immutable, and active suffix x(() of length Ng. which is the target of the current refinement step. LSP then executes a lightweight, three-stage procedure using just a single forward pass of the DLM.

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Single-Pass Prediction and Stability Assessment. The process begins with single forward pass of the model po on the current composite state (xf²) xx This pass yields logits for all Nx positions in the active suffix. From these logits, compute stability diagnostic for each position We use the logit margin, defined as the difference between the top-two logit
i E
values:
(1) The margin serves as a simple yet effective low-cost proxy for the model's local decisiveness. A large margin indicates that the model has high confidence in its top prediction for token relative to all alternatives, suggesting this token is stable and unlikely to change in subsequent refinement steps. Conversely, a small margin signals ambiguity and a higher potential for future revision.
6, 20))(0) (1).
Distinction from Blockwise Autoregressive Decoding, A crucial distinction must be made be- tween LSP and standard Blockwise Autoregressive (AR) decoding. In Blockwise AR, a block is generated greedily and frozen; the model never observes "future" tokens during that block's gener- ation. In contrast, LSP preserves the fundamental advantage of DLMs: bidirectional lookahead.
During every diffusion step, the model performs forward pass the composite state (x (x)))
The active suffix (() fine the tokens in the candidate block based the global context of the future sequence, resolving narrative and logical dependencies before the prefix is committed.
A acts as a noisy, bidirectional lookahead buffer. This allows the model to re-
Approximate KV Caching for Prefix States. In strict bidirectional model, the internal represen- tations (KV pairs) of the prefix tokens theoretically depend on the active suffix tokens. Recomputing the entire sequence at every step, however, defeats the purpose of caching. LSP employs an approxi- mate KV caching strategy, treating the committed prefix as fixed context. This is supported by recent findings in diffusion acceleration (Wu et al., 2025), which demonstrate that KV activations exhibit high similarity across adjacent inference steps, and reusing cached KVs for stable tokens results in a negligible performance drop while unlocking massive systemic speedups.
Targeted Block Sizing via Adaptive Thresholding. Using a fixed stability threshold to accept tokens is brittle; threshold that aggressive for one model or task may be too conservative for another. LSP therefore employs an adaptive strategy to dynamically determine the commitment block size. The goal is to ensure that the active sequence length .Ng decays at a steady, geometric rate, which is the key to achieving near-quadratic total work complexity.
To achieve this, we define L'(r) as the length of the longest consecutive run of positions, starting from the beginning of the active suffix, whose logit margins all exceed a given threshold Instead of fixing t, LSP efficiently searches for a threshold тыe such that the resulting block length L' L'(T)) falls within target fractional range of the current active sequence length:
T'(TR) E [aNNe, (NNa),
B < 1 are user-specified fractions (e.g., a 0.25, 3 0.50). The parameter prevents overly cautious steps that would slow down convergence, while 3 prevents overly aggres- sive commitments that might introduce errors. This search can be implemented efficiently in O(N)) time by first computing the prefix- mreii--mnimumm of the margin scores and then selecting target length m E [[aNN] 1, [] that satisfies the condition. This adaptive sizing allows LSP be aggres- sive when the model is confident and conservative when it is uncertain, ensuring robust and rapid progress.
where 0
Structural Coherence via Boundary Snapping and Monotone Progress. Committing block of tokens that ends mid-word or mid-sentence creates an unnatural and incoherent context for the subsequent generation step, potentially requiring costly repairs. To enhance global coherence, LSP trims the candidate block of length L'(TE) to a more natural structural boundary. Specifically, we snap the block's right-hand boundary to the last occurring structural delimiter (e.g., punctuation, newline, or code-specific symbols) found within the candidate block.
Let D be set of such delimiters, Lminn 2 1 be minimum guaranteed block size. and W 2 0 be lookback window. The final commitment length L is determined as:
L A max (mminn max < L' 0j E DDL' MAL'-jSW]}
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Algorithm 1 LSP (LSP): Longest Stable Prefix Scheduler
1: Input: DLM pe, delimiter set D, acceptance interval [a, 3], min length Luin. snap window W.
2: State: Frozen prefix X <- prompt; Active suffix XA + masked suffix; Cache IC <- CACHEINIT(X,,
3: while N < X > do
4: logits t- pppppppFFFFp (A;
Single pass over active suffix
5: Compute 01:N and di.N from logits.
6: Choose 7 s.t. ['(r) E [N via prefix-min selection.
7:
I' + L'(T); L f SHAPTODELIMITER((I.. D, Lmin: W).
8:
if = then
9:
L+1
Fallback to ensure progress
10:
end
11: Commit Ø1.L: X + X5 BiLL XA XA(L+11)
12: + APPENDTOCACHE(( f1:1)
D Contiguous KV append
13:
end while
14:
Return X
This snapping mechanism intelligently trades a few tokens of immediate progress for significantly improved downstream coherence, reducing the need for future revisions. To guarantee termination, no suitable delimiters are found and the candidate block shorter than Lmin- a fallback rule ensures that at least one token is committed (L <- 1). This guarantees that the frozen prefix Xr grows monotonically in every iteration.
The complete, integrated procedure is detailed in Algorithm 1. to a virtuous cycle: monolithic prefix absorption preserves KV cache contiguity, which enables efficient attention. Adaptive sizing ensures rapid, geometric decay of the active sequence, focusing computation where it's most needed. Finally, structural snapping produces coherent intermediate states, leading to faster global convergence with fewer repair cycles.
By design, each step contributes
EXPERIMENTS
4.1 EXPERIMENTAL SETUP
Models and Benchmarks. Our empirical evaluation is conducted two prominent open-source Diffusion Language Models, LLaDA-8B (Nie et al., 2025) and Dream-7B (Ye et al., 2025), to demonstrate the general applicability of scheduling approach. We select focused but chal- lenging set of benchmarks where the generation of coherent, long-form text with strong inter- nal dependencies is paramount. For assessing performance mathematical reasoning, GSM8K (Cobbe et al., 2021), dataset of grade-school math word problems where correctness de- pends valid chain of thought. Performance measured by answer. For code generation, a domain that demands strict syntactic and logical correctness, we em- ploy the widely-used HumanEval (Chen et al., 2021) and MBPP (Austin al., 2021b) benchmarks. Success on these tasks is measured by the pass@1 I metric, which evaluates whether the generated code passes a set of unit tests. ensure deterministic and reproducible results, all experiments utilize a zero-shot prompting setup and employ greedy decoding.
match accuracy of the final
Baseline and LSP Configuration. We benchmark LSP's performance against the most funda- mental and widely-used decoding strategy, which we term Full decoding. This baseline repre- sents the standard iterative refinement process of DLM, using the complete step budget available (Tmax T., where I. is the generation length). The 'Full' baseline serves as the reference for gen- eration quality and provides the 1.0x anchor for our speedup calculations. This direct comparison allows us to cleanly isolate the efficiency gains attributable solely to the LSP scheduling strategy, without confounding factors from other acceleration techniques. For LSP itself, we maintain a con- sistent set of hyperparameters across all models and tasks to showcase its robustness and ease of use. The fractional acceptance interval is set to Ja, 3 = [0.25, 0.50], encouraging steady, geometric decay of the active suffix. We use a minimal block length of Lmin = to guarantee progress and a structural snapping window of W 16 tokens, modest value chosen balance coherence with

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Table 1: Main benchmark results on LLaDA-8B and Dream-7B. We report the task-specific score
(%) and the inference speedup over the 'Full' baseline. LSP delivers substantial speedups while maintaining or even improving task performance.
LLaDA-8B
Dream-7B
Benchmark
Full
LSP (Ours)
Full
LSP (Ours)
General Tasks
MMLU
54.1
54.2
(2.32x)
67.6
66.4
(2.12x)
ARC-C
83,2
83.3
(1.91x)
88.1
88.0
(2.28x)
Hellaswag
68.7
70.7
(2.18x)
81.2
82.1
(2,53x)
TruthfulQA
34.4
45.8
(2.29x)
55.6
53.5
(1.86x)
WinoGrande
73.8
70.7
(1.74x)
62.5
62.3
(1.47x)
PIQA
80.9
82.1
(2.02x)
86.1
86.4
(2.31x)
Mathematics & Scientific
GSM8K
77.1
77.6
(1.51x)
75.3
75.4
(1.69x)
GPQA
25.2
25.5
(1.79x)
27.0
26.4
(1.68x)
Code
HumanEval MBPP
30.5
29.3
(1.22x)
54.9
55.5
(1.46x)
37.6
37.6
(1.33x)
54.0
54.6
(1.48x)
Planning Tasks
Countdown
15.3
15.3
(2.63x)
14.6
15.1
(2.40x)
Sudoku
35.0
36.0
(3.00
89.0
88.0
(3.36x)
aggressive commitment. These parameters were determined from brief, one-time validation sweep on a small subset of the GSM8K dataset.
4.2 MAIN RESULTS AND ANALYSIS
Table presents the main results our evaluation. The findings clearly show that LSP provides massive acceleration in inference speed-up to 3.4x- preserving the high generation quality of the full-budget baseline. In some cases, LSP even slightly improves performance, demonstrat- ing its effectiveness as robust and efficient decoding scheduler. On the GSM8K mathematical reasoning task, LSP achieves a 1.5x speedup with LLaDAA-8B while also delivering a marginal improvement accuracy (+0.5%). This suggests that by committing stable prefix of the reasoning chain early, LSP can prevent noisy, late-stage refinement steps from corrupting an already correct solution.
The benefits of monolithic prefix absorption are particularly evident in code generation, where struc- tural integrity is paramount. On HumanEval, LSP accelerates inference by 1.2x with a negligible impact on the success rate. This confirms that the prefix-first topology, augmented by structural snapping, is highly effective at generating coherent, syntactically valid code blocks more efficiently than iterative, full-sequence refinement. The results on Dream-7B show similar trend, with even more substantial speedups, underscoring the general applicability of the LSP scheduling principle across different model architectures.
4.3 ABLATION STUDIES AND ANALYSIS
To rigorously dissect the contributions of LSP'ss core components, conduct series of ablation studies on the challenging GSM8K benchmark using the LLaDA-8B model. These experiments are designed to isolate the impact of each design choice-adaptin adaptive sizing, structural snapping, and the prefix-firs topology-4e validate that our method's remarkable effectiveness stems from a princi- pled, synergistic design rather than any single factor.

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Table 2: Ablation on Sizing Strategy (GSM8K, LLaDA-8B). Fixed-size commitment strategies are brittle, forcing trade-off between the number of inference steps (speed) and final accuracy. LSP's adaptive sizing dynamically finds the most effective balance.
Strategy
GSM8K Score (%)
Total Steps (Avg.)
Fixed Prefix (1 tokens)
67.1
128
Fixed Prefix (2 tokens)
66.8
64
Fixed Prefix (4 tokens)
47.6
Fixed Prefix (8 tokens)
19.3
16
Adaptive (LSP)
69.9
68
4.3.1 THE CRITICAL ROLE OF ADAPTIVE SIZING
Motivation. A core hypothesis of our work is that model's confidence not uniform throughout the generation process. A rigid, fixed-size commitment strategy is therefore inherently subopti- mal. Such a strategy is blind to the model's internal state: it will be either too conservative during high-confidence phases (leading to excessive number of refinement steps) too aggressive dur- ing uncertain phases (introducing errors that degrade quality). Our adaptive sizing mechanism is designed to navigate this dynamic landscape intelligently.
Analysis. To test this hypothesis, compare the standard adaptive LSP against variants that commit a fixed-size prefix at each step, ranging from a cautious one token to an aggressive 8. As demonstrated in Table 2, the fixed-size strategies are brittle, exposing sharp trade-off between efficiency and accuracy.
Committing minimal prefix (1 or 2 tokens) is an overly conservative approach. While it preserves high accuracy by taking cautious, small steps, it requires large number of iterations to complete the sequence, resulting low efficiency. Conversely, committing large fixed block tokens) is overly aggressive. It drastically reduces the number of steps, making it very fast, but does so by prematurely committing unstable, low-margin tokens, leading significant drop in final accuracy. The 2-token strategy offers reasonable, but still suboptimal, compromise.
LSP's adaptive approach elegantly resolves this dilemma. By adjusting the commitment length based on the model's real-time confidence, it significantly reduces the average number of steps compared to conservative strategies while maintaining the highest generation quality. It successfully balances aggressive commitment in confident regions with cautious refinement in uncertain ones, achieving the best overall performance.
4.3.2 ENHANCING COHERENCE WITH STRUCTURAL SNAPPING
Motivation. Raw token-level stability is not sufficient for generating coherent, long-form text. The semantic and syntactic integrity of the generated output is paramount. Committing a prefix that ends abruptly mid-statement, mid-expression, even mid-word creates an unnatural and confusing context for the model's subsequent refinement step. Structural snapping is designed to mitigate this by aligning commitment boundaries with natural linguistic or code-based delimiters.
Analysis. We evaluate the impact of this mechanism by disabling it, which results in a greedier strategy that always commits the full candidate block T.' identified by adaptive sizing. The results in Table 3 are unambiguous. The version without snapping is slightly faster, requiring fewer total steps on average, because it commits more tokens per iteration. However, this aggressive approach comes at significant cost to quality, with a noticeable drop in the final score. The reason is that committing incoherent prefixes (e.g.. 'the final answer is 3.141') pollutes the context for subsequent denoising steps. This forces the model expend its capacity correcting these unnatural boundaries rather than generating new, coherent content, ultimately leading to more errors. The small efficiency cost of snapping slightly higher step count) is overwhelmingly justified by the substantial gain in
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Table Ablation studies core LSP components (GSM8K, LLaDA-8B), Both structural snap- ping and the prefix-frst topology are crucial for achieving high performance. Each component is compared against the full LSP method.
Method
Score (%)
Total Steps (Avg.)
Ablation on Structural Snapping
LSP w/o Snapping
67.8
~5
Full LSP (Ours)
69.9
~68
Ablation on Commitment Topology
Scattered-Margin
68.9
128
Full LSP (Ours)
69.9
~68
generation quality. This confirms that structural snapping is crucial component for maintaining high-quality, coherent output within the LSP framework.
4.3.3 PREFIX-FIRST vs. SCATTERED: THE POWER TOPOLOGY
Motivation. Finally, we directly test our central thesis: that the topology of commitment primary driver of efficiency in DLM inference. We construct a strong baseline, "Scattered-Margin" which uses LSP's margin-based adaptive sizing to determine how many tokens to commit, but then accepts the confident tokens from anywhere in the active sequence. following the conventional scattered acceptance paradigm. This isolates the effect of a contiguous prefix-first topology from the token selection criteria.
Analysis. Table 3 provides direct and compelling evidence for the superiority of the prefix-firs topology. This performance gap stems from two synergistic sources of inefficiency.
Algorithmic Instability: The scattered approach creates numerous unstable "holes" and internal boundaries between frozen and masked tokens. This forces the diffusion model to reconcile dis- parate, non-local contexts in every step. leading to slower and less stable convergence. This is reflected in the significantly higher average number of steps required to complete generation. In contrast, LSPPs prefix-fire first topology maintains a single, clean boundary, allowing the model focus its capacity on coherently extending stable prefix.
Systemic Inefficiency: The performance difference is magnified the hardware level. With prefix-first topology, the Key-Value (KV) cache for the frozen prefix is contiguous in memory. It can be computed once and efficiently reused, with new states being appended in simple, fast operation. A scattered topology. however, completely fragments the KV cache. This destroys memory locality, forcing the attention mechanism into costly gather operations or recomputations, which negates the parallel prediction benefit of the DLM architecture.
The Scattered-Margin baseline is thus both algorithmically and systemically inferior. Our results confirm that monolithic prefix absorption is the key turning the parallel prediction power of DLMs into fast and effective generation on modern hardware.
4.3.4 QUANTIFYING REPAIR COSTS VIA TOKEN FLIP RATE
A potential concern with early commitment is that freezing a prefix might restrict the model's ability correct early mistakes, thereby increasing the "repair cost" in the active suffix. To investigate this, we measure the Flip Raee-the percentage of tokens in the active suffix that change their top-1 prediction between consecutive diffusion steps. During the mid-stage of generation (25%- 75% completion), the standard Scattered baseline exhibits high Flip Rate of 14.2%, as the model constantly oscillates to reconcile a fragmented context. In contrast, under LSP, the Flip Rate in the remaining suffix plummets to just 4.3%. This empirical evidence proves that resolving and freezing a coherent prefix actually stabilizes the future generation context, drastically reducing the required repair operations rather than increasing them.

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Published as a conference paper at ICLR 2026
25
Scattered Baseline
LSP (Ours)
20
18.5%
19.1%
Token Flip Rate (%)
1.5
14.2%
9.8%
10
.4.%%
Early (0-25%)
Mid (25-75%)
Late (75-100%)
Stage Generation
Figure 2: Quantifying Repair Costs via Token Flip Rate. We measure the percentage of tokens in the active suffix that change their top prediction between consecutive diffusion steps. While the scattered baseline forces the model constantly reconcile a fragmented context (maintaining high flip rates), LSP locks in a coherent prefix early. This stabilizes the future generation context, drastically reducing token oscillations and repair costs in the mid-to-late stages (from 14.2% down to 4.3%)
CONCLUSION
In this work, we identified scattered token acceptance as primary algorithmic and systemic bot- tleneck that throttles the practical inference speed of Diffusion Language Models. To address this, we introduced the Longest Stable Prefix (LSP) scheduler, training-free,, model-agnostic inference principle centered on monolithic prefix ubsorption. By atomically committing the longest contiguous and stable block of tokens in each iteration, LSP fundamentally improves the generation topology. Our empirical results demonstrate that LSP substantially accelerates inference across diverse models and challenging benchmarks, such code generation and mathematical reasoning, while preserv- ing or even slightly improving task performance. This work validates that principled commitment strategy is key to unlocking the parallel generation promise of DLMs, bridging the gap between their theoretical potential and practical efficiency. While our experiments validate the effectiveness of LSP prominent open-source DLMs, the current implementation relies on a simple yet effective logit margin as stability proxy; future work could investigate more sophisticated, temporally camporally-wwae aware stability metrics that might offer better trade-off between commitment aggression and accuracy. Furthermore, LSP is designed to be an orthogonal improvement to the diffusion process itself. A investigate synergy with other acceleration techniques,
promising avenue for future research such speculative decoding approximate caching methods, potentially achieve compounding gains in inference speed. Finally, the efficacy structural snapping was demonstrated on tasks with clear delimiters (code, reasoning steps), and its impact more open-ended, creative generation tasks warrants further investigation.
Limitations While LSP is highly effective for sequential (left-to-right) generation, its contigu- ous prefix assumption is not inherently suited for non-sequential tasks such as text in-filling or unconstrained editing. Extending the topological principles of LSP support "stable islands" for bidirectional in in-filling remains an exciting avenue for future work. Additionally, our current imple- mentation of structural snapping relies heuristic delimiter sets. While robust across English and CJK domains, future iterations could integrate lightweight, learned boundary- head to provide tokenizer-agnostic structural alignment.
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Published as a conference paper at ICLR 2026
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APPENDIX
THE USE OF LARGE LANGUAGE MODELS (LLMS)
LLMs were used exclusively as writing assistance tools in preparing this manuscript. Specifically, we employed LLMs for grammar checking. All research ideation, experimental design, analysis, and scientific conclusions are entirely the work of the authors. The LLMs played no role in the conception of research questions, methodology development, or interpretation of results. Authors take full responsibility for all content in this paper, including any text refined with LLM assistance.
Table 4: Visualization LSP's monolithic prefix absorption for math reasoning (Granular View). Each colored block represents the Longest Stable Prefix atomically committed in single step. This more detailed breakdown shows how LSP iteratively extends the solution by committing shorter, coherent chunks. The strict left-to-right contiguous growth (light dark green) is main- tained, and commit boundaries align with natural linguistic or mathematical units (e.g., clauses, calculations), demonstrating LSP's structural snapping in action.
Task
LSP Generation Process (Committed Prefixes per Step)
Prompt:
Natalia sold clips of her friends. She sold 8 clips each friend. Then she bought 15 more clips. How many clips does Natalia have now?
Natalia sold 8 clips to each of her 4 friends.
This means she sold total of
4 = 32 clips.
She then bought 15 more clips,
so she now has 32 + 15
47 clips.
The final answer is 47.
Prompt:
John has 12 apples. He gives half to Mary. Then Mary buys twice as many apples as she received from John. How many apples does Mary have now?
John gives half of his 12 apples Mary,
so Mary receives 12 apples.
Then Mary buys twice the number she received,
which is 2 6 12 apples.
Mary now has her original
plus the 12 she bought,
for a total + 12 = 18 apples.
Answer: 18.
13


Reviews:
[{"review_id": "pxdsACWrHL", "reviewer": "Reviewer_kHHK", "summary": "This paper identifies \"scattered acceptance\" as a primary bottleneck hindering the inference speed of Diffusion Language Models (DLMs), arguing that it leads to both algorithmic inefficiency and severe KV cache fragmentation. To address this, the authors propose the Longest Stable Prefix (LSP), a training-free and model-agnostic scheduling paradigm based on monolithic prefix absorption. In each step, LSP atomically commits the longest possible contiguous and stable prefix of the active sequence, identified via an adaptive, confidence-based mechanism and aligned to natural structural boundaries. This prefix-first topology maintains a contiguous KV cache and ensures a geometric decay in the computational workload. Experiments on challenging code and reasoning tasks demonstrate that LSP substantially accelerates inference (up to 3.4x) while preserving, and in some cases improving, generation quality.", "questions": "In Figure 1, the diagram for t=0 shows a sequence of logit margins starting with [0.2, 0.8, 0.4, 0.6, ...]. It then states that a stability threshold (τ) of 0.6 is chosen, resulting in a commitment of 3 tokens. This appears inconsistent with the paper's definition of a stable prefix.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. The left-to-right commitment strategy dramatically improves KV cache efficiency.\n  \n2. The adaptive sizing mechanism intelligently modulates generation speed based on model confidence, achieving a superior speed-quality balance compared to fixed-size strategies.\n  \n3. The method achieves significant inference acceleration without sacrificing, and in some cases even improving, generation quality.\n  \n4. Its training-free and model-agnostic nature makes the method highly practical and broadly generalizable across different DLMs.", "weaknesses": "1. **Limited Comparative Baselines:** The empirical evaluation primarily compares LSP against \"Full decoding,\" which serves as a quality baseline rather than a competitive speed-oriented one. The paper does not include a direct comparison against other contemporary DLM acceleration techniques, making it difficult to position LSP's performance within the existing state-of-the-art.\n  \n2. **Insufficient Hyperparameter Analysis:** The paper lacks a sensitivity analysis for its key hyperparameter, the fractional acceptance interval [α, β]. While the authors claim this parameter is robust, no data is provided to substantiate this, leaving the tuning effort required for new models or tasks an open question.", "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": "uwF1oFFJwD", "reviewer": "Reviewer_Yt8W", "summary": "The paper proposes a training-free approach for improving inference efficiency in diffusion language models (DLMs) by dynamically selecting the longest stable prefix based on confidence measured over a decoding window, thereby reducing cache fragmentation and redundant computations. The method achieves faster and more coherent generation compared to standard DLM decoding schedules.", "questions": "- What motivates the geometric decay assumption for suffix-length determination?\n- Can the approach generalize to non-sequential or in-fill decoding tasks?\n- How sensitive is the thresholding to model scale or dataset domain?\n- Could the authors provide a breakdown of runtime gains (cache locality vs. token reuse)?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Simple and effective approach that mitigates cache fragmentation without retraining.\n- Practical efficiency gains demonstrated across multiple pretrained DLMs.\n- Clear experimental reporting and consistent evaluation settings.\n- Compatible with existing architectures, requiring minimal modification.", "weaknesses": "- The main novelty lies in using left windowed confidence instead of position-wise confidence, which is conceptually similar to autoregressive commitment heuristics.\n- The prefix-first decoding constraint may limit diffusion’s flexibility for editing, in-fill, or parallel token generation tasks.\n- The geometric decay rule for active suffix length and its thresholding lacks theoretical or empirical grounding.\n- GSM8K is a relatively simple benchmark for 7B-scale models; evaluating on AMC or AIME would better assess reasoning capability.\n- Table 1 could include more detail on what contributes to the speedup (e.g., cache locality vs. adaptive thresholding).\n- The robustness of suffix-length selection across model scales, sequence lengths, and task domains is not discussed.", "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": "QwLl106fWc", "reviewer": "Reviewer_jKnz", "summary": "Identifies scattered acceptance as a key bottleneck in improving efficiency of DLMs causing slow gather operations.\nProposes:\n1. LSP scheduler, where prefixes of tokens are committed instead of scattered commitment. This ensures the KV cache is not fragmented leading to efficient computation reuse.\n2. Adaptive thresholding to find the longest stable prefix instead of using a fixed threshold.\n3. Structural boundary snapping\n\nThe results show significant speedup and at the same time some quality gains that support the strength of the proposed changes.", "questions": "- See weakness.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Identifies an important problem\n- Proposes a practical and elegant solution, especially because it is training free.\n- Demonstrates strong speedup performance and sometimes slight quality gains.\n- Thorough ablation studies.", "weaknesses": "- The proposed method is less of a DLM and more of a blockwise autoregressive decoding.\n- The additional proposals (structural snapping) are not optional solutions, they are critical patches to get blockwise decoding to work.\n- Structural snapping is domain specific and might not perform well always. How is the performance on CJK?\n- The prefix commitment is irreversible, which means one of the most important advantages of DLMs is gone.\n- There is no mention on KV cache update of the committed sequence later on since bidirectional attention can impact it.\n- Tasks that need more fixing of the previously generated sequence (for example, creativity tasks) should be evaluated upon.", "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": "S2yKSVZccp", "reviewer": "Reviewer_Cvwn", "summary": "The paper fixes “scattered acceptance” in DLM decoding by committing one contiguous left-aligned block each step via the Longest Stable Prefix (LSP): compute per-token margins in a single pass, choose a threshold to absorb ~25–50% of the active suffix, snap to delimiters, and atomically commit. This maintains a single frozen/active boundary, keeps KV cache contiguous, and empirically cuts latency/denoiser calls on LLaDA-8B and Dream-7B with near-parity quality (GSM8K, GPQA, HumanEval, MBPP).\n\nMy primary expertise is outside language diffusion models. I’ve done a careful read, but please weigh my field-specific comments accordingly.", "questions": "See the weaknesses part.", "limitations": "", "rating": 10, "confidence": 1, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The single prefix-first boundary is an elegant topology that aligns algorithmic coherence with KV-cache locality. \n\n2. The design is concrete—margin-based stability, adaptive thresholds, delimiter snapping, and a guaranteed-progress fallback.\n\n3. Empirically it yields 1.5–3× speedups with near-parity quality across reasoning and code tasks, with ablations isolating each component’s effect.", "weaknesses": "1. LSP’s delimiter snapping introduces heuristic dependencies that could be brittle across tokenizers and vocabularies.\n\n2. Theoretical framing is light, with no formal bounds on early-commit errors or convergence.\n\n3. The evaluation does not quantify repair costs when early-committed tokens later require substantial rewriting.", "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)