Answer First, Reason Later: Commitment Order in Diffusion LLMs

# Commitment Order in Diffusion LLMs
Source: [https://arxiv.org/html/2608.05687](https://arxiv.org/html/2608.05687)
## Answer First, Reason Later: Commitment Order in Diffusion LLMs

Jewon Yeom1Jaewon Sok2Seonghyeon Park3 Jeongjae Park1Hwiyeong Lee1Taesup Kim1, 1Graduate School of Data Science, Seoul National University 2Department of Rural Systems Engineering, Seoul National University 3Department of Aerospace Engineering, Seoul National University

###### Abstract

Diffusion large language models \(dLLMs\) can commit tokens in any order—a freedom marketed as their core advantage over autoregressive decoding\. We show that on reasoning tasks this freedom is instead the axis of failure\. Logging every commitment during decoding of LLaDA\-8B on GSM8K, we find that unconstrained \(*pure*\) decoding freezes the final answer within the first quarter of the trajectory, while most of the reasoning region is still masked, and collapses to answer\-only outputs on up to90%90\\%of problems as the canvas grows\. The cause is not the model’s termination beliefs—EOS “pressure” is nearly identical across decoders—but*reachability*: whether the sampler may act on those beliefs at distant positions\. A2×22\{\\times\}2prompt–decoder design shows that chain\-of\-thought helps*only*under ordered commitment: the interaction is roughly3535percentage points, and without reasoning text the two decoders are indistinguishable\. We decompose this into a collapse channel and an order channel and replicate it on Dream\-7B and MATH\-500\. A single\-knob intervention—frontier\-gated commitment, with no training and no change to the model’s output distribution—causally recovers the full gap while preserving up to4×4\\timesparallel decoding, along a measured frontier whose optimal window flips from strictly left\-to\-right at full refinement to unconstrained at eight tokens per step\. Our results reframe existing window\-style samplers, previously motivated by efficiency, as the minimal fix for a reasoning pathology they were never designed to address\.

## 1Introduction

Diffusion large language models \(dLLMs\) generate text by iteratively unmasking a canvas of positions, committing at each denoising step the tokens the model is most confident about—anywhere in the sequence\(Austinet al\.,[2021](https://arxiv.org/html/2608.05687#bib.bib1); Nieet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib2)\)\. We study the masked variety exclusively, the family to which both open models we use belong, and write dLLM throughout\. This*any\-order*freedom is the family’s signature: it enables native infilling, bidirectional conditioning, and parallel token commitment, and it is routinely cited as the reason to prefer diffusion over left\-to\-right autoregression\. That the freedom is not free has recently become apparent:Niet al\.\([2026](https://arxiv.org/html/2608.05687#bib.bib18)\)show that arbitrary\-order generation narrows a dLLM’s reasoning potential during reinforcement learning, because confidence\-ordered sampling defers the high\-entropy connectives on which exploration depends\. We arrive at a convergent conclusion from the opposite end of the pipeline\. Studying inference alone—no training, no reward—we show that commitment order determines whether chain\-of\-thought functions at all, identify the two failure modes through which it does so, trace both to a single sampler property, and remove them with a one\-knob decoding constraint whose price we measure\.

One of the two pathologies we study is already on record\.Nieet al\.\([2025](https://arxiv.org/html/2608.05687#bib.bib2)\)report that unconstrained decoding loses roughly nine points to block\-wise sampling on GSM8K, and attribute the loss to<eos\>padding in the fine\-tuning data causing early termination\. Instrumenting the decoding loop of LLaDA\-8B\-Instruct to log, for every position,*when*it is committed and*what*the model predicted there at every step, we find that effect in a more extreme form and a second one beside it\. The first is*answer\-only collapse*: the model skips reasoning entirely, emitting a bare answer followed by padding, on more than a third of problems at a 256\-token canvas and nine tenths at 512—giving it more room makes reasoning*less*likely to appear\. The second is*answer\-first commitment*: even when reasoning is produced, the answer freezes in the first quarter of the trajectory while the median reasoning token is committed near the halfway point, and the derivation is then backfilled around an already\-fixed conclusion, its arithmetic errors aimed at reaching it\. In one case the model writes a correct sum*after*committing an answer that contradicts it, with no way to revise either\. Block\-sequential \(semi\-autoregressive\) decoding of the*same*model exhibits neither pathology\.

The standard explanation is the EOS bias of dLLM training\(Nieet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib2); Kimet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib10); Liuet al\.,[2026](https://arxiv.org/html/2608.05687#bib.bib11)\): padding teaches the model to want EOS late in the canvas\. We find it incomplete\. EOS*pressure*—the fraction of masked positions whose top prediction is EOS—is nearly identical across decoders, while EOS*commitment*differs by more than a factor of two\. The model wants to terminate equally in both cases; only the unconstrained sampler is*able*to act on that want hundreds of tokens ahead\. The pathology lives in reachability, not belief, which is why remedies that retrain away the pressure address a symptom, and why a decoding\-time fix should suffice\.

Does any of this affect task performance, or is chain\-of\-thought text epiphenomenal to a dLLM’s answer? We answer with a2×22\{\\times\}2design fixed in advance, crossing prompt \(request reasoning vs\. answer\-only\) with decoder \(pure vs\. semi\-AR\) on 250 paired problems\. The interaction is large—about3535percentage points, permutationp<10−4p<10^\{\-4\}—and its structure is diagnostic: in the answer\-only column the decoders are statistically indistinguishable, so the entire semi\-AR advantage is conditional on reasoning text existing\. The same chain\-of\-thought that buys3131points under ordered commitment buys nearly nothing under pure decoding, though not*less*than nothing: a failed prediction of ours shows pure CoT still contributes a small positive effect, so reasoning under any\-order decoding is*attenuated*, not decorative\. We decompose the interaction into a*collapse channel*and an*order channel*, and replicate the full pattern—including the answer\-only near\-tie—on Dream\-7B\(Yeet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib23)\)and on MATH\-500, where short answers cannot be guessed, collapse nearly vanishes, and the order channel operates alone\.

If commitment order is the mechanism, constraining only the order should recover the loss\. We gate commitment eligibility to a window ofwwpositions ahead of the left\-most masked position—no training, no logit modification, a single knob interpolating pure \(w=∞w\{=\}\\infty\) and left\-to\-right \(w=1w\{=\}1\)\. Window\-restricted decoding is not new; it exists in the efficiency literature as a cache and parallelism device\(Zuoet al\.,[2026](https://arxiv.org/html/2608.05687#bib.bib14); Shuet al\.,[2026](https://arxiv.org/html/2608.05687#bib.bib15)\)\. We use it as a*manipulated variable*\. Everyw≤64w\\leq 64lifts pure decoding from0\.5280\.528to0\.820\.82–0\.850\.85, indistinguishable from semi\-AR, with a sliding window of 32 matching a block of 32 to within a point—the active ingredient is reachability, not block structure\. Recovery is largest where reasoning matters: on the hardest tail the gate restores nearly all of the gap, and the answers that flip concentrate on high\-step problems\. Order is not free, however\. Sweeping the compute budget reveals a crossover between four and eight tokens per step: at full refinement the optimal window isw=1w\{=\}1and any\-order freedom buys nothing, while at eight tokens per step the constraint is purely harmful with no interior optimum—the optimal commitment window flips between extremes with the number of refinement steps\. Within the useful regime, a gated decoder retains near\-AR accuracy at a measured4×4\\timeswall\-clock speedup\.

Our contributions are threefold\. We correct the standard account of a known failure and add a second one beside it: answer\-only collapse is not driven by the model’s EOS beliefs, which are decoder\-invariant, and answer\-first backfill has gone unremarked; both follow from unrestricted long\-range commitment \(§[3](https://arxiv.org/html/2608.05687#S3), §[4](https://arxiv.org/html/2608.05687#S4)\)\. Through a2×22\{\\times\}2prompt–decoder design we show that whether chain\-of\-thought functions at all is determined by commitment order, replicated across two models and two datasets, and decompose the effect into collapse and order channels \(§[5](https://arxiv.org/html/2608.05687#S5)\)\. And we give a single\-knob intervention that causally recovers the full order channel while preserving up to4×4\\timesparallel decoding, quantifying the accuracy–parallelism frontier and explaining why existing window\-style samplers work \(§[6](https://arxiv.org/html/2608.05687#S6)\)\. Two of our advance predictions failed; both are reported where they arise, alongside the pipeline validation checks in Appendix[B](https://arxiv.org/html/2608.05687#A2)\.

## 2Related work

#### EOS overflow and length pathologies\.

Our collapse phenomenon intersects a fast\-growing line on dLLM termination failures\.Kimet al\.\([2025](https://arxiv.org/html/2608.05687#bib.bib10)\)name the<eos\>overflow effect—longer budgets yielding shorter responses—and trace it to<eos\>’s dual role as terminator and padding;Liuet al\.\([2026](https://arxiv.org/html/2608.05687#bib.bib11)\)decouple the roles with a dedicated padding token;Yanget al\.\([2025](https://arxiv.org/html/2608.05687#bib.bib13)\)retrain EOS placement for variable\-length decoding\. Inference\-side work reads EOS density as a length signal\(Yanget al\.,[2026](https://arxiv.org/html/2608.05687#bib.bib12)\)or suppresses EOS so it cannot win the confidence competition early\(Yuet al\.,[2026b](https://arxiv.org/html/2608.05687#bib.bib26)\)\. All of this locates the pathology in the model’s termination*beliefs*; our dissociation \(§[3\.3](https://arxiv.org/html/2608.05687#S3.SS3)\) shows those beliefs are near\-identical across decoders that do and do not collapse, and that what differs is commitment*reachability*—which is why a decoding\-time constraint suffices where these works retrain\.

#### Window\- and block\-restricted decoding\.

Our intervention has mechanical precedents\. Windowed schemes restrict computation near the generation frontier for caching and parallelism\(Zuoet al\.,[2026](https://arxiv.org/html/2608.05687#bib.bib14)\); block diffusion interpolates between autoregression and diffusion architecturally\(Arriolaet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib25)\); and semi\-AR block decoding ships as the recommended configuration for reasoning benchmarks, on the stated grounds that unconstrained decoding terminates early under<eos\>\-padded fine\-tuning\(Nieet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib2); LLaDA Team,[2025](https://arxiv.org/html/2608.05687#bib.bib32)\)\. That recommendation is where our question begins: it settles*that*blocks help without establishing*what*in them helps, or what the help is worth\. Closest to our mechanism,Shuet al\.\([2026](https://arxiv.org/html/2608.05687#bib.bib15)\)anchor a confidence\-aware window at the left\-most masked token so tokens near block boundaries are not forced to commit without context, reporting gains averaging1\.41\.4points over block decoding\. On the training side,Arriola and Kuleshov \([2026](https://arxiv.org/html/2608.05687#bib.bib16)\)bias the learned order distribution toward left\-to\-right, andWanget al\.\([2026b](https://arxiv.org/html/2608.05687#bib.bib27)\)argue the useful left\-to\-right bias in language is*token\-local*\. The window is thus known as a refinement*within*ordered decoding, and locality as a training\-time prior; our question is prior to both—whether order matters at all\. Sweepingwwfrom11to∞\\infty, the endpoint these works do not consider, unconstrained decoding, is where a thirty\-point effect and two qualitative failure modes live\.

#### Order, faithfulness, and dLLM analysis\.

That models can decide first and rationalize afterwards is well documented for autoregressive LLMs—via biased\-context interventions\(Turpinet al\.,[2023](https://arxiv.org/html/2608.05687#bib.bib3)\), CoT truncation\(Lanham and others,[2023](https://arxiv.org/html/2608.05687#bib.bib4)\), probes that decode the answer long before the chain ends\(Boppanaet al\.,[2026](https://arxiv.org/html/2608.05687#bib.bib24)\), answer\-conditioned stress tests\(Jianget al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib21)\), and RL penalizing probe\-detected “reasoning theater”\(Parekh,[2026](https://arxiv.org/html/2608.05687#bib.bib22)\)\. All must*infer*pre\-commitment, because an AR model’s answer appears after its reasoning; our setting inverts this, since the commitment log records causal order directly\. Within dLLMs, analysis tools\(Wanget al\.,[2026a](https://arxiv.org/html/2608.05687#bib.bib19); Lu,[2026](https://arxiv.org/html/2608.05687#bib.bib20)\)and trajectory\-search test\-time scaling\(Baiet al\.,[2026](https://arxiv.org/html/2608.05687#bib.bib17)\)take the sampler’s freedom as given\. A separate family attacks our root cause—irreversible commitment—by making commitments revisable, either through remasking\(Wanget al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib28)\)or by re\-ranking every position each step so a visible token may be overwritten\(Yuet al\.,[2026b](https://arxiv.org/html/2608.05687#bib.bib26)\); notably the latter reports that revision capacity*hurts*a pretrained model until post\-training aligns confidence with self\-generated context, and diagnoses the same mechanism we do, that surrounding text accommodates a wrong committed token until confidence in the error grows\. Where they let the model take a commitment back at the cost of training, we prevent the premature commitment with none\. Closest in spirit isNiet al\.\([2026](https://arxiv.org/html/2608.05687#bib.bib18)\), who argue arbitrary order*limits*rather than expands reasoning potential: confidence\-ordered unmasking defers high\-entropy connectives, so branch points are filled after their options are fixed, degrading the exploration reinforcement learning depends on; their remedy constrains the RL policy to left\-to\-right trajectories\. Ours is the inference\-time counterpart\. They identify an ordering pathology in what the model learns to explore; we identify two in what a fixed model emits, localize both to reachability rather than beliefs, establish causality with a prompt×\\timesdecoder interaction rather than downstream RL performance, and obtain the fix without training, at a measured cost in parallelism\.

A reading in the opposite direction is offered byYuet al\.\([2026a](https://arxiv.org/html/2608.05687#bib.bib31)\), who find masked dLLMs*robust*to answer\-first prompting where autoregressive models are not, and attribute this to confidence\-ordered sampling deferring hard answer tokens\. Their configuration overlaps ours closely, so we reconcile the two in Appendix[E](https://arxiv.org/html/2608.05687#A5): their own timings show answers exposed within the first5%5\\%of the trajectory at easy difficulty levels, with deferral confined to the hardest, and the quantity they defend is accuracy under a*reordered prompt*rather than across decoders\.

## 3Answer\-only collapse

### 3\.1Setup and instrumentation

Our primary model is LLaDA\-8B\-Instruct\(Nieet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib2)\); §[5\.3](https://arxiv.org/html/2608.05687#S5.SS3)replicates all headline results on Dream\-7B\(Yeet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib23)\)\. We evaluate on GSM8K\(Cobbe and others,[2021](https://arxiv.org/html/2608.05687#bib.bib5)\)\(first 500 test problems; paired comparisons use the first 250\) and MATH\-500\(Hendrycks and others,[2021](https://arxiv.org/html/2608.05687#bib.bib6); Lightman and others,[2024](https://arxiv.org/html/2608.05687#bib.bib7)\)\.

We compare two decoders of the*same*model under identical prompts and budgets\.*Pure*diffusion decoding treats the canvas ofLLpositions as one region: at each step the sampler commits the highest\-confidence predictions anywhere\.*Semi\-autoregressive*\(semi\-AR\) decoding fills blocks of 32 positions strictly left to right, with free diffusion inside each block—the configuration shipped with LLaDA\-8B’s official demo\. Unless noted,L∈\{256,512\}L\\in\\\{256,512\\\}, the number of denoising steps equalsLL, and we use the official low\-confidence remasking sampler at temperature0, which is deterministic; Appendix[A](https://arxiv.org/html/2608.05687#A1)shows all signs are preserved under stochastic sampling atT=0\.7T\{=\}0\.7across three seeds\.

We re\-implement the official sampling loop with logging hooks, verified token\-identical to the reference implementation \(ndiff=0=0\)\. For every position we record its commitment stepτ​\(i\)\\tau\(i\), committed token, and confidence; per step, aggregate statistics over still\-masked positions; and every 16 steps, a snapshot of top\-1 predictions\. A*commitment*is the irreversible unmasking of a position, and since the sampler never revises,τ\\tauis well defined\. The*answer span*is located by a fixed regex cascade and mapped to positions via tokenizer offsets; an output exhibits*answer\-only collapse*if that span is detected but the preceding reasoning region is essentially empty of non\-EOS tokens \(Appendix[B](https://arxiv.org/html/2608.05687#A2)\)\.

### 3\.2Answer\-only collapse

The phenomenon itself is known to the models’ authors\.Nieet al\.\([2025](https://arxiv.org/html/2608.05687#bib.bib2)\)report that block\-wise sampling scores78\.678\.6on GSM8K against69\.469\.4for unconstrained decoding, and attribute the gap to<eos\>padding in the SFT data causing early termination; the official sampling guidelines add that at large answer lengths low\-confidence remasking yields “an unusually high proportion of<eos\>tokens”\(LLaDA Team,[2025](https://arxiv.org/html/2608.05687#bib.bib32)\), an observation repeated for other instruction\-tuned dLLMs\(Yang and others,[2025](https://arxiv.org/html/2608.05687#bib.bib33)\)\. Our logs put numbers on it and, more importantly, set up the measurement that discriminates between explanations\. Under pure decoding, LLaDA\-8B skips reasoning entirely—emitting a bare “The answer isXX” followed by an EOS stream—on 36\.6% of problems atL=256L\{=\}256and 90\.2% atL=512L\{=\}512, while semi\-AR decoding of the same model, prompt, and budget collapses on 2\.2% and 5\.6% \(Fig\.[5](https://arxiv.org/html/2608.05687#A3.F5), Appendix[C](https://arxiv.org/html/2608.05687#A3)\)\. The gap we measure is far larger than the nine points reported at the shorter answer lengths of the original evaluation, which is itself consistent with the canvas dependence\. The phenomenon is not an artifact of deterministic decoding: atT=0\.7T\{=\}0\.7the pure collapse rate is unchanged at 90\.8% on the paired subset, and it is the*same problems*that collapse—the collapse sets atT=0T\{=\}0andT=0\.7T\{=\}0\.7overlap at Jaccard0\.9960\.996\(227 shared problems; the stochastic set is a strict subset of the deterministic one, differing by a single problem\)\. Collapse is a per\-problem deterministic property, invariant to sampling noise \(Appendix[A](https://arxiv.org/html/2608.05687#A1)\)\.

Collapsed outputs are, surprisingly,*more*accurate in aggregate than non\-collapsed ones \(0\.749 vs\. 0\.478 atL=256L\{=\}256\)—a selection effect, since collapse concentrates on easy problems \(gold reasoning steps 2\.58 vs\. 4\.08,p≈10−36p\\approx 10^\{\-36\}\) where a direct guess often succeeds\. The cost appears against ordered decoding: pure 0\.528 vs\. semi\-AR 0\.844 \(n=250n\{=\}250, McNemarp=1\.4×10−16p\{=\}1\.4\\times 10^\{\-16\}\), and among the rare non\-collapsed pure outputs accuracy falls to 0\.091 \(n=22n\{=\}22\)—a deficit §[4](https://arxiv.org/html/2608.05687#S4)traces to*how*that reasoning is produced\.

### 3\.3The pressure–commitment dissociation

Why does only one decoder collapse? The canonical answer, given byNieet al\.\([2025](https://arxiv.org/html/2608.05687#bib.bib2)\)and repeated across the EOS\-overflow literature \(§[2](https://arxiv.org/html/2608.05687#S2)\), is that responses are padded with EOS during supervised fine\-tuning, inflating its marginal probability at late positions so that confidence\-ordered samplers commit it early\. That account is about what the model has learned to want\. It is incomplete, because the wanting does not differ between the decoders that do and do not collapse\. Define EOS*pressure*at stepttas the fraction of still\-masked positions whose top\-1 prediction is EOS—a property of the model’s beliefs, computed identically under any decoder—and EOS*commitment*as the fraction of positions actually finalized as EOS\. AtL=512L\{=\}512, pressure is nearly identical across decoders \(0\.782 vs\. 0\.766\) while commitment differs by more than2×2\\times\(0\.912 vs\. 0\.444\)\. The model*wants*to terminate equally in both cases; only the unconstrained sampler can*act*on that want hundreds of tokens ahead of any generated content\. Once distant EOS tokens are committed, bidirectional attention propagates the signal leftward and the space in which reasoning could have appeared is consumed—the encroachment documented byLiuet al\.\([2026](https://arxiv.org/html/2608.05687#bib.bib11)\), here shown to be gated by reachability rather than driven by pressure\.

The practical implication is immediate: because the pathology lives in what the sampler may do rather than in what the model believes, no retraining is required to remove it\. Restricting*where*commitments may land—leaving the model and its distribution at eligible positions untouched—should suffice, a prediction §[6](https://arxiv.org/html/2608.05687#S6)confirms causally\.

## 4Answer\-first commitment and backfilled reasoning

Collapse explains outputs with no reasoning\. This section explains the outputs*with*reasoning—and why, under pure decoding, that reasoning barely helps \(0\.091 accuracy among non\-collapsed outputs; §[3\.2](https://arxiv.org/html/2608.05687#S3.SS2)\)\. The answer is again written in the commitment log: the conclusion is committed first, and the derivation is generated afterwards, conditioned on it\.

### 4\.1The answer freezes first

![Refer to caption](https://arxiv.org/html/2608.05687v1/figures/fig1_teaser.png)Figure 1:Commitment order, read off the log\.\(a\) The order in which one GSM8K response \(\#39\) was written under each decoder\. Each cell is a fortieth of the response in reading order; the number is*when*it was committed and the colour encodes the same \(dark early, light late\)\. Under pure decoding the answer cell \(boxed\) is written third, before most of the derivation; under semi\-AR the response is written in reading order and the answer comes last\. \(b\) The behavioral consequence \(GSM8K \#183, pure\)\. The model sums60\+57\+54\+5160\{\+\}57\{\+\}54\{\+\}51correctly to222222, then rewrites the total as212212so that220−212220\-212meets the answer88it had already frozen; the correct chain gives22\. The timeline underneath gives the order in which these parts were written: the answer and the rewritten total commit near step270270, the correct arithmetic only near step460460\. Single run, official sampler atT=0T\{=\}0\.Figure[1](https://arxiv.org/html/2608.05687#S4.F1)summarizes commitment timing\. Under pure decoding, the answer span is committed at a median normalized stept∗t^\{\*\}of 0\.147 \(L=256L\{=\}256\) and 0\.240 \(L=512L\{=\}512\), while the median*reasoning*token is committed near0\.5050\.505: the conclusion freezes when roughly half of the derivation does not yet exist\. Under semi\-AR decoding the order inverts \(reasoning0\.2630\.263, answer0\.5510\.551\)—but we flag this row as a*by\-construction baseline*rather than a finding: left\-to\-right blocks force position to determine time, so reasoning\-before\-answer follows from the layout of the text\. The substantive observation is confined to pure decoding, where nothing forces any order and the model chooses answer\-first\.

The same logs quantify how far pure decoding strays from left to right\. The Spearman correlation between position and commitment time is0\.2740\.274\(L=256L\{=\}256\) and0\.6300\.630\(L=512L\{=\}512\) under pure decoding, against0\.9990\.999for semi\-AR—though the latter is largely arithmetic, since block structure alone bounds rank error\.111Random within\-block order still yieldsρ≈0\.996\\rho\\approx 0\.996at block size 32\.The informative number is*within*blocks, where semi\-AR is unconstrained:ρ=0\.969\\rho=0\.969\. That confidence\-ordered decoding tracks left\-to\-right on content tokens has been reported independently byYao \([2026](https://arxiv.org/html/2608.05687#bib.bib30)\), who find confidence\-first reveal paths nearly identical to forced left\-to\-right; our measurement confirms it inside blocks and adds the contrast that matters here—given a clean left context the model orders itself at short range, so its disorder, and its pathology, are specifically long\-range\.

### 4\.2Backfill: reasoning conditioned on a frozen conclusion

Once the answer is committed it is immutable by the sampler’s rules—and it is not merely a plan but*literal context*, attended bidirectionally at every subsequent step\. Reasoning generated aftert∗t^\{\*\}is therefore answer\-conditioned generation; we call this regime*backfill*\.

Backfill mirrors the belief–action dissociation of §[3\.3](https://arxiv.org/html/2608.05687#S3.SS3)at the level of committed tokens\. The model’s*belief*about the answer forms equally early under both decoders \(comparable pre\-commitment lead,\+0\.055\+0\.055–0\.0940\.094normalized steps, in every mode\); what differs is when the sampler*acts*—absolute first\-match time0\.0620\.062under pure decoding versus0\.4690\.469under semi\-AR\. Ordered decoding does not stop the model from guessing early; it stops the guess from becoming context\.

The behavioral signature of backfill is that errors in the derivation are*aimed*\. A representative case \(GSM8K \#183, Fig\.[1](https://arxiv.org/html/2608.05687#S4.F1)b\): the model adds60\+57\+54\+5160\+57\+54\+51step by step and reaches222222correctly, then on the very next line rewrites the total as212212, so that220−212220\-212lands exactly on the already\-committed answer88; the correct chain gives22\. The commitment log removes any ambiguity about direction\. The answer and the rewritten total freeze at step∼270\{\\sim\}270of512512, while the correct stepwise arithmetic is back\-filled around step∼460\{\\sim\}460—so the model produces, later in the same trajectory, a computation that contradicts its own answer, and has no mechanism to act on it\. This is not an isolated curiosity\. Re\-evaluating every parsed arithmetic equation, non\-collapsed pure outputs contain incorrect equations at a32\.8%32\.8\\%rate, versus3\.8%3\.8\\%for semi\-AR and2\.52\.5–2\.7%2\.7\\%for the gated decoder of §[6](https://arxiv.org/html/2608.05687#S6);8282–92%92\\%of pure decoding’s erroneous equations are written*after*the answer commits, and5757–66%66\\%are load\-bearing—the erroneous value is precisely what the committed answer requires\.222Parsing fails on2929–36%36\\%of outputs, so we read these rates as indicative\. The post\-answer share is structurally zero for semi\-AR, whose answer commits last, and is excluded from that comparison\.Conversely, answers*unsupported*by the reasoning are rare \(5\.75\.7–9\.1%9\.1\\%\): the model does not ignore its derivation—it bends the derivation to meet the conclusion\.

It is tempting to close the argument correlationally: early answers should predict wrong answers\. The data refuse, instructively\. Answer\-first commitment is*universal*under pure decoding—when the answer freezes, a mean78\.7%78\.7\\%of the reasoning region is still masked, and even the least premature quartile exceeds70%70\\%—so with no non\-premature control group, timing cannot correlate with correctness, and it does not \(r=0\.057r\{=\}0\.057,p=0\.32p\{=\}0\.32; difficulty\-partialedr=0\.015r\{=\}0\.015\)\.333A second trap runs the other way: under semi\-AR,*wrong*answers commit*later*\(p=3\.3×10−5p\{=\}3\.3\\times 10^\{\-5\}\), an artifact of left\-to\-right layout wheret∗t^\{\*\}proxies response length and hence difficulty\. We decline to interpret it\.Establishing that commitment order*causes*the deficit therefore requires manipulating it while holding everything else fixed, which the next two sections do\.

## 5Chain\-of\-thought helps only under ordered commitment

Sections[3](https://arxiv.org/html/2608.05687#S3)–[4](https://arxiv.org/html/2608.05687#S4)establish*that*pure decoding writes the answer first; this section establishes that it*matters*\.

### 5\.1Design and result

We cross two prompts with two decoders on 250 paired GSM8K problems: the*CoT*prompt elicits a derivation followed by “The answer isXX”, the*direct*prompt forbids reasoning and requests only the answer\. Nothing is injected or post\-edited—in all four cells the model generates its own text—so the manipulated variable is whether reasoning text may exist, crossed with the order in which commitments may land\. Predictions were fixed before the runs, including the one below that failed\.

Table 1:Prompt×\\timesdecoder interaction \(GSM8K,n=250n\{=\}250paired,L=512L\{=\}512\)\. Without reasoning text the decoders are indistinguishable; with it, they diverge by3131points\.Δ​Δ=\+34\.8​pp\\Delta\\Delta=\+34\.8\\,\\mathrm\{pp\}\[26\.8,42\.8\]\[26\.8,42\.8\], permutationp<10−4p<10^\{\-4\}\.![Refer to caption](https://arxiv.org/html/2608.05687v1/figures/fig3_interaction.png)Figure 2:Chain\-of\-thought helps only under ordered commitment\.Left: the2×22\{\\times\}2on LLaDA\-8B \(n=250n\{=\}250paired\); in the direct column the decoders are indistinguishable\. The annotation gives the interactionΔ​Δ\\Delta\\Deltawith its bootstrap 95% confidence interval in brackets\. Center: the interaction grows monotonically with difficulty \(gold\-step tertiles; error bars are bootstrap 95% CIs\)\. Right: the same pattern on Dream\-7B, including the direct\-column near\-tie\.Table[1](https://arxiv.org/html/2608.05687#S5.T1)and Fig\.[2](https://arxiv.org/html/2608.05687#S5.F2)contain the paper’s central inference, and its sharpest cell is the one where nothing happens: in the*direct*column, pure and semi\-AR are statistically indistinguishable \(0\.5640\.564vs\.0\.5320\.532\)\. Semi\-AR is not a stronger decoder; stripped of reasoning text it has no advantage at all, and its entire\+31\.6​pp\+31\.6\\,\\mathrm\{pp\}CoT\-setting edge is the value of reasoning*unlocked by order*\. Two secondary predictions sharpen this\. Pure decoding returns the*same answer*regardless of what the prompt asks far more often than semi\-AR \(0\.6960\.696vs\.0\.5080\.508,p=6×10−8p\{=\}6\\times 10^\{\-8\}\): when the answer is an early guess, requesting a derivation does not change it\. And the interaction grows monotonically with difficulty \(\+16\.5\+16\.5/\+45\.5\+45\.5/\+69\.6​pp\+69\.6\\,\\mathrm\{pp\}across gold\-step tertiles\), so pure decoding forfeits most exactly where derivations are long\.

One prediction failed, and the failure calibrates the claim: we predicted CoT would be*useless*under pure decoding, but once collapse is accounted for it contributes\+8\.9​pp\+8\.9\\,\\mathrm\{pp\}\(p=0\.029p\{=\}0\.029\)\. Reasoning under any\-order decoding is therefore*attenuated*, not decorative—it captures a fraction of a value on the order of\+40​pp\+40\\,\\mathrm\{pp\}, and commitment order gates the remainder\.

### 5\.2Two channels

The interaction aggregates two mechanistically distinct losses, separated with a length manipulation\. Shrinking the canvas fromL=512L\{=\}512toL=256L\{=\}256cuts pure decoding’s collapse rate from90%90\\%to37%37\\%while changing little else, and the interaction shrinks in step from\+34\.8\+34\.8to\+21\.2​pp\+21\.2\\,\\mathrm\{pp\}\. The difference,\+13\.6​pp\+13\.6\\,\\mathrm\{pp\}\[2\.4,24\.8\]\[2\.4,24\.8\], is the*collapse channel*: reasoning never produced cannot help\. The residual\+21\.2​pp\+21\.2\\,\\mathrm\{pp\}is the*order channel*: reasoning that*is*produced, but backfilled around a frozen answer, recovers only a fraction of its value—among non\-collapsed CoT outputs the decoder gap remains0\.4780\.478vs\.0\.7940\.794\(n=316n\{=\}316,p≈3×10−20p\\approx 3\\times 10^\{\-20\}\)\. Both channels share one root—unrestricted long\-range commitment—but differ in signature: absent text versus impotent text\.

### 5\.3Generality: a second model and a second dataset

Dream\-7B\(Yeet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib23)\)is initialized from an autoregressive model, and its inference code still carries a next\-token convention as a fossil of that ancestry—if a strong local left\-to\-right prior could prevent answer\-first pathology, this is where it should\. It does not: pure\-decoding collapse is88\.0%88\.0\\%\(vs\.90\.8%90\.8\\%\), and the2×22\{\\times\}2pattern reappears withΔ​Δ=\+38\.4​pp\\Delta\\Delta=\+38\.4\\,\\mathrm\{pp\}\[30\.8,46\.0\]\[30\.8,46\.0\]and the direct\-column near\-tie intact \(\+2\.0​pp\+2\.0\\,\\mathrm\{pp\},p=0\.511p\{=\}0\.511\)\. The near\-coincidence of point estimates is chance; the claim is sign, magnitude class, and overlapping intervals\.

MATH\-500 removes the other ingredient: its answers cannot be guessed in a few tokens and the collapse channel all but vanishes \(90\.8%→13\.6%90\.8\\%\\to 13\.6\\%\), so collapse is a*conjunction*of unrestricted reachability \(a sampler property\) and a guessably short answer \(a task property\)\. That leaves a natural low\-collapse regime in which the order channel operates alone—the decoder gap is\+16\.8​pp\+16\.8\\,\\mathrm\{pp\}\(p=1\.2×10−8p\{=\}1\.2\\times 10^\{\-8\}\), consistent with the\+21\.2​pp\+21\.2\\,\\mathrm\{pp\}residual on GSM8K—while backfill persists: pure decoding fills the canvas with derivation \(median length 510\) yet commits the answer att∗=0\.275t^\{\*\}\{=\}0\.275against a median reasoning token at0\.5060\.506\(Appendix[C](https://arxiv.org/html/2608.05687#A3)\)\.

## 6Frontier\-gated commitment: recovery and its price

### 6\.1The order channel is causal

#### A one\-knob manipulation\.

Letf​\(t\)f\(t\)be the left\-most masked position at steptt\.*Frontier gating*restricts commitment eligibility to masked positionsi<f​\(t\)\+wi<f\(t\)\+w: the sampler still scores every position and selects by confidence, and its distribution at eligible positions is untouched—only*where*commitments may land is constrained\. The knob interpolates the designs of interest:w=∞w\{=\}\\inftyis pure decoding exactly \(verified token\-identical\), andw=1w\{=\}1enforces left\-to\-right order\. Window\-restricted decoding is not itself new \(§[2](https://arxiv.org/html/2608.05687#S2)\); what has not been asked is what the window does relative to*unconstrained*decoding—the regime our sweep includes, and where the effect is an order of magnitude larger and qualitative rather than incremental\. We stress that the gate is not offered as a replacement for semi\-AR decoding, which already ships and performs comparably throughout our results\. Its role is that of a manipulated variable: semi\-AR differs from pure decoding in several respects at once, while sweepingwwmoves reachability alone and shows that reachability by itself is sufficient\. We usewwas a manipulated variable: if the order channel of §[5\.2](https://arxiv.org/html/2608.05687#S5.SS2)is causal, constraining reachability alone should recover it\.

![Refer to caption](https://arxiv.org/html/2608.05687v1/figures/fig4_wsweep.png)Figure 3:Constraining reachability alone recovers the order channel\.Left: accuracy vs\. frontier windowww\(GSM8K,n=250n\{=\}250paired, Wilson 95% CIs\); everyw≤64w\\leq 64matches semi\-AR, and slidingw=32w\{=\}32matches block 32 within1\.2​pp1\.2\\,\\mathrm\{pp\}\. Right: on the hardest subset \(problems 141–249\), where pure decoding scores 0\.459, gating restores 93–100% of the gap\.
#### Recovery\.

It does \(Fig\.[3](https://arxiv.org/html/2608.05687#S6.F3)a\)\. Everyw≤64w\\leq 64lifts pure decoding from0\.5280\.528to0\.8240\.824–0\.8520\.852\(ppvs\. pure between10−1510^\{\-15\}and10−1910^\{\-19\}\), indistinguishable from semi\-AR’s0\.8440\.844, and collapse falls from90\.8%90\.8\\%to2\.42\.4–8\.4%8\.4\\%\. Two comparisons localize the active ingredient\. A*sliding*window of 32 matches a*block*of 32 within1\.2​pp1\.2\\,\\mathrm\{pp\}\(replicated on Dream\-7B\), so block boundaries contribute nothing—the recommendation to decode in blocks\(Nieet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib2)\)is, on this evidence, a recommendation to restrict reachability\. And recovery concentrates where reasoning matters: on the hardest tail \(problems 141–249, pure0\.4590\.459\) gating restores9393–100%100\\%of the gap, the gain is larger on hard problems than easy \(\+38\.5\+38\.5vs\.\+27\.6​pp\+27\.6\\,\\mathrm\{pp\}\), and the answers that flip are the high\-step problems \(p∼10−15p\\sim 10^\{\-15\}\)—the interventional mirror of the observational gradient in §[5\.1](https://arxiv.org/html/2608.05687#S5.SS1)\.

#### Rescuing a few\-shot configuration\.

The intervention also transfers to a setting we did not design\. Under a standard 8\-shot GSM8K CoT prompt\(Weiet al\.,[2022](https://arxiv.org/html/2608.05687#bib.bib29)\), Dream\-7B’s native sampler collapses in our harness \(0\.3660\.366\) and unconstrained decoding reaches only0\.5090\.509, while adding the gate yields0\.8210\.821, the range Dream\-7B reports—a within\-harness contrast under a prompt of our choosing, not a reproduction of its evaluation configuration \(Appendix[B](https://arxiv.org/html/2608.05687#A2)\)\. The gradient is instructive: few\-shot exemplars*partially*mitigate collapse \(88%→58%88\\%\\to 58\\%\) while the decoding constraint nearly eliminates it \(1\.8%1\.8\\%\)\.

The sweep’s most provocative cell isw=1w\{=\}1: strict left\-to\-right order is the*best*setting \(0\.8520\.852\), so at full refinement any\-order freedom buys nothing on this task—raising the obvious objection of why to use a diffusion decoder at all\. Answering it requires paying for order in the currency diffusion is supposed to save\.

### 6\.2The accuracy–parallelism frontier

![Refer to caption](https://arxiv.org/html/2608.05687v1/figures/fig5_pareto.png)Figure 4:The accuracy–parallelism frontier\(GSM8K,n=250n\{=\}250paired\)\. \(a\) Accuracy vs\. NFE for the three decoders\. The top axis is measured wall\-clock time on one A100\-SXM4\-40GB at batch 1, linear in NFE \(R2=1\.00R^\{2\}\{=\}1\.00\), so the horizontal axis is equivalently a time axis; shading marks the regime in which pure decoding leads\. \(b\) At NFE 64, widening the frontier window plateaus*below*the unconstrained endpoint \(w=512≡w\{=\}512\\equivpure, open marker\): no interior optimum exists in this regime\.Figure[4](https://arxiv.org/html/2608.05687#S6.F4)sweeps the number of denoising steps\. Down to 4 tokens/step, ordered decoders convert compute into accuracy gracefully \(gated retains0\.7160\.716at a4×4\\timesbudget reduction,\+21\.6​pp\+21\.6\\,\\mathrm\{pp\}over pure,p=10−8p\{=\}10^\{\-8\}\); at 8 tokens/step they cross*below*pure\. We predicted the opposite and report the miss\. The low\-NFE side is not what the aggregate suggests\. Pure decoding is nearly NFE\-*insensitive*—accuracy moves only0\.4760\.476–0\.5360\.536across an8×8\\timesbudget range—because it collapses on72\.8%72\.8\\%of problems even at NFE 64 and so never uses the refinement steps\. Conditioning on outputs that actually contain a chain of thought, every decoder converges to the same accuracy at 8 tokens/step:0\.3090\.309\(pure\),0\.2990\.299\(gatedw=16w\{=\}16\),0\.3020\.302\(semi\-AR\)\. Pure leads in aggregate only because collapse selects the easy problems on which a bare guess succeeds\. The crossover therefore does not show that order constraints become harmful at low NFE; it shows that coherent reasoning is*not generable*at 8 tokens/step, and that unconstrained decoding evades this by not attempting it\. What the ordered decoders produce instead is a third failure mode: token\-level corruption—duplicated words, digit garble, repetition, truncation—from committing adjacent tokens before their neighbors’ context resolves\.

Nor can the crossover be escaped by widening the window: at NFE 64, accuracy overw∈\{16,64,128,512≡pure\}w\\in\\\{16,64,128,512\{\\equiv\}\\text\{pure\}\\\}runs0\.308→0\.392→0\.376→0\.4760\.308\\to 0\.392\\to 0\.376\\to 0\.476, a plateau strictly below the unconstrained endpoint with no interior optimum\. Nor by scheduling it: a window widened in proportion to the per\-step commit demand matches fixedw=1w\{=\}1at full refinement but gains nothing at reduced budgets, and—diagnostically—does not reduce degeneration \(Appendix[D](https://arxiv.org/html/2608.05687#A4)\)\. The damage is a matter of commit*density*, not window availability\. Combined with thew=1w\{=\}1optimum at full refinement, the picture is symmetric:*the optimal commitment window flips between extremes with the number of refinement steps*, and order buys accuracy only when there are enough steps to exploit it\.

The frontier’sxx\-axis is real time: wall\-clock is linear in NFE \(R2=1\.00R^\{2\}\{=\}1\.00\) and decoder\-invariant to within1\.5%1\.5\\%, since gating is a boolean mask\. The operating point follows—a gated decoder at 4 tokens/step retains near\-AR accuracy at a measured4×4\\timesspeedup—and past it, no ordering policy we tested converts further parallelism into anything but noise\.

## 7Discussion

Two models bracket the hypothesis that a stronger left\-to\-right prior might prevent answer\-first pathology\. The prior is real—LLaDA\-8B proceeds left to right of its own accord inside a block, and Dream\-7B inherits an autoregressive habit strong enough to survive in its inference code—yet Dream\-7B still collapses at88%88\\%\. The resolution is a mismatch of scales: training\-induced order bias is*token\-local*, while collapse is a*canvas\-scale*event—an EOS committed hundreds of positions ahead of any generated content\. This is why the remedy is cheap, gating at the scale of the pathology, and whyw=1w\{=\}1costs nothing at full refinement; the same argument organizes our three failure modes as one commitment policy failing along different axes \(Appendix[E](https://arxiv.org/html/2608.05687#A5)\)\.

Several bounds apply: our tasks are mathematical reasoning, so whether the order channel operates in open\-ended generation, code, or retrieval\-grounded settings is untested; main tables use single deterministic runs, with signs verified under sampling and paraphrase \(Appendix[A](https://arxiv.org/html/2608.05687#A1)\); and Dream\-7B comparisons are within\-harness\. What remains is that any\-order generation, these models’ advertised advantage, is on reasoning tasks the axis of their failure—not in what they believe but in what their samplers may do with those beliefs\.

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## Appendix ARobustness

#### R1: stochastic sampling\.

Main tables use the official sampler atT=0T\{=\}0\. Repeating the three\-decoder comparison atT=0\.7T\{=\}0\.7with three seeds preserves every sign: pure collapse exceeds 50% and ordered decoders stay below 20% in every seed; paired decoder gaps remain positive and significant;\|\|gated−\-semi\-AR\|≤5pp\|\\leq 5\\,\\mathrm\{pp\}\. Collapse is not merely equal in rate but identical in*membership*: theT=0T\{=\}0andT=0\.7T\{=\}0\.7collapse sets overlap at Jaccard0\.9960\.996\(227 shared problems out of 228 and 227\), with the stochastic set a strict subset\. We asked in advance whether temperature would mitigate collapse, without betting on a direction; it does not\.

#### R2: prompt paraphrase\.

Re\-running the full2×22\{\\times\}2with paraphrased CoT and direct instructions \(wording frozen before the runs\) givesΔ​Δ′=\+29\.1​pp\\Delta\\Delta^\{\\prime\}=\+29\.1\\,\\mathrm\{pp\}\[20\.9,37\.2\]\[20\.9,37\.2\]and a direct\-column difference of0\.4​pp0\.4\\,\\mathrm\{pp\}\(p=1\.00p\{=\}1\.00\)—the near\-tie is if anything cleaner than with the original wording\.

#### R3: latency\.

Wall\-clock per problem on a single A100 \(batch 1\), 20 problems per cell after warmup: 31\.96/15\.99/7\.99/4\.00 s for pure at 512/256/128/64 steps, with semi\-AR and gated within1\.5%1\.5\\%at every budget \(R2=1\.00R^\{2\}=1\.00against a linear fit in NFE\)\. Per\-step cost is thus independent of how many tokens are committed, so the NFE axis of Fig\.[4](https://arxiv.org/html/2608.05687#S6.F4)is a measured time axis, and the choice of decoding policy is free in wall\-clock terms\.

## Appendix BReproducibility

#### Models and hardware\.

Two instruction\-tuned masked dLLMs, loaded inbfloat16with remote code enabled undertransformers4\.49\.0, on a single A100\-SXM4\-40GB at batch size 1:

> GSAI\-ML/LLaDA\-8B\-Instructaccessed 2026\-07\-22Dream\-org/Dream\-v0\-Instruct\-7Baccessed 2026\-07\-26

Neither checkpoint was pinned to a revision—both were loaded from the default branch—so we record access dates in lieu of commit hashes\.

#### Data\.

GSM8K\(Cobbe and others,[2021](https://arxiv.org/html/2608.05687#bib.bib5)\),maintest split: problems0–499499for single\-decoder statistics,0–249249for all paired comparisons\. MATH\-500\(Lightman and others,[2024](https://arxiv.org/html/2608.05687#bib.bib7)\): problems0–249249, level distribution22/52/52/64/6022/52/52/64/60for levels11–55\.

#### Decoding configurations\.

Every cell is fully specified by \(model,LL, steps, block length or windowww, prompt, temperature\) and recorded in a per\-run configuration file\. Main tables:L=512L\{=\}512, steps=512\{=\}512, temperature0, no classifier\-free guidance; pure decoding is block length=L\{=\}L, semi\-AR is block length3232, gated is frontier windowwwwith block length=L\{=\}L\. The canvas\-length manipulation of §[5\.2](https://arxiv.org/html/2608.05687#S5.SS2)repeats the2×22\{\\times\}2atL=256L\{=\}256, steps=256\{=\}256\. The compute sweep of §[6\.2](https://arxiv.org/html/2608.05687#S6.SS2)varies steps over\{256,128,64\}\\\{256,128,64\\\}atL=512L\{=\}512\. For Dream\-7B, the only code difference is a family flag that applies the one\-position logit shift used by its own generation code; the sampling policy is otherwise identical across models by design\.

#### Frontier gating\.

At each denoising step, letffbe the index of the left\-most masked position\. Candidate positions are the masked positionsiiwithi<f\+wi<f\+w; the sampler computes confidences over all positions as usual but restricts top\-kkcommitment selection to candidates\. The candidate set is never empty, sinceffitself is always a candidate\. At the final step of each block all remaining masked positions are flushed, which is a no\-op wheneverwwis at least the generation length\. Settingw≥Lw\\geq Lreproduces unconstrained decoding token\-for\-token\.

#### Prompts\.

Every prompt is assembled as the problem statement, a blank line, and a single instruction, after which the model’s own chat template is applied withadd\_generation\_prompt=True\. The instructions are verbatim:

> CoT\.Finish your response with "The answer is X", where X is the final answer\. Direct\.Respond with only the final answer in the form "The answer is X"\. Do not include any reasoning, explanation, or intermediate steps\. CoT paraphrase\.End your response with the line "The answer is X", where X is the final answer\. Direct paraphrase\.Give only the final answer, written as "The answer is X"\. Do not include any working, reasoning, or intermediate steps\. MATH\-500\.Finish your response with the final answer in the form\\\\backslashboxed\{X\}\.

The few\-shot condition of §[6\.1](https://arxiv.org/html/2608.05687#S6.SS1)uses the canonical eight GSM8K chain\-of\-thought exemplars\(Weiet al\.,[2022](https://arxiv.org/html/2608.05687#bib.bib29)\), joined by blank lines in the formQuestion: \{q\}/Answer: \{a\}, followed by the target question and the CoT instruction above, all as a single user message\. The first exemplar reads:

> Question: There are 15 trees in the grove\. Grove workers will plant trees in the grove today\. After they are done, there will be 21 trees\. How many trees did the grove workers plant today? Answer: There are 15 trees originally\. Then there were 21 trees after some more were planted\. So there must have been 21 \- 15 = 6\. The answer is 6\.

#### Answer extraction and scoring\.

Extraction uses a fixed cascade applied to the full generated text—\\\\backslashboxed\{\}, then “the answer is”, then the last number—and the matched string is mapped back to token positions via tokenizer offsets\. GSM8K is scored by normalized numeric exact match against the gold value after\#\#\#\#\. MATH\-500 is scored by normalized exact string match \(whitespace only; no case or symbol substitution\)*or*symbolic verification, applied identically to all cells; we report both this rule and the verifier\-only variant, which differ by3/0/13/0/1problems across the three cells\.

#### Validation\.

Three checks bound the trustworthiness of the reported numbers\.*Sampler equivalence*: our instrumented loop reproduces the reference implementation token\-for\-token \(ndiff=0=0\) under identical seeds, re\-verified after the multi\-model refactor together with a 20/20 match against stored outputs from a previously completed cell—so the logging hooks and the family flag leave the LLaDA\-8B sampling path unchanged\.*Commit\-schedule accounting*: gated low\-NFE cells initially left∼\\sim7 of 512 positions unresolved, because the frontier window can starve the per\-step commit budget; after adding a block\-final flush, unresolved positions went to 0 and degeneration fell from33%33\\%to20%20\\%, while accuracy moved from0\.3000\.300to0\.3080\.308\. The artifact was therefore not the cause of the low\-NFE deficit, and all reported numbers use the fixed cells\.*Native calibration*: to check that a single fixed loop does not cripple Dream\-7B, we compared it against Dream\-7B’s own sampler on the same problems—custom pure0\.3670\.367\(512 steps\) versus native0\.4170\.417\(256 steps; the budgets differ because of a session limit, and unconstrained decoding is nearly NFE\-insensitive\), a gap of−5\.0​pp\-5\.0\\,\\mathrm\{pp\}\. Because the loop is held fixed across models by design, this gap is documented rather than tuned away\.

#### Artifacts\.

All reported numbers derive from a frozen snapshot of9,2299\{,\}229files \(178\.6178\.6MB\) with a per\-number mapping from each reported figure to its source cell and analysis script; the manifest has SHA\-2566355e996e70e4eebceb031315fc72bc66e067aa6f56c82fcbe257c5e0fc92359\. Robustness runs are stored in a separate namespace so that main\-table provenance is unambiguous\. Code, per\-problem summaries, configurations, and the figure\-regeneration scripts are available at[https://github\.com/Scuttie/dllm\-commitment\-order](https://github.com/Scuttie/dllm-commitment-order)\.

## Appendix CGenerality: full replication details

![Refer to caption](https://arxiv.org/html/2608.05687v1/figures/fig2_collapse.png)Figure 5:Collapse and its cause\.Left: answer\-only collapse by decoder and canvas length \(GSM8K,n=500n\{=\}500\); a longer canvas makes pure decoding*less*likely to reason\. Accuracies for these cells are0\.576/0\.5000\.576/0\.500\(pure,L=256/512L\{=\}256/512\) and0\.824/0\.8440\.824/0\.844\(semi\-AR\)\. Right: the dissociation atL=512L\{=\}512—EOS*pressure*\(fraction of masked positions predicting EOS\) is nearly identical across decoders, while EOS*commitment*differs by2×2\\times\.#### Dream\-7B\-7B\.

We ran Dream\-7B through the same instrumented loop, adding only a family flag that applies the one\-position logit shift its own generation code uses\. Before adopting any number we regression\-gated the refactor against LLaDA\-8B \(token\-identical vanilla decoding,ndiff=0=0; 20/20 match against stored outputs from a previously completed cell\) and calibrated against Dream\-7B’s native sampler \(§[B](https://arxiv.org/html/2608.05687#A2)\)\. Final2×22\{\\times\}2\(n=250n\{=\}250paired\): pure0\.3760\.376\(CoT\) /0\.3760\.376\(direct\); semi\-AR0\.7800\.780/0\.3960\.396\. Collapse88\.0%88\.0\\%under pure,16\.8%16\.8\\%under semi\-AR\. Gating atw=32w\{=\}32reaches0\.7680\.768,\+39\.2​pp\+39\.2\\,\\mathrm\{pp\}over pure \(p=3\.5×10−24p\{=\}3\.5\\times 10^\{\-24\}\) and within1\.2​pp1\.2\\,\\mathrm\{pp\}of semi\-AR \(p=0\.508p\{=\}0\.508\), replicating the sliding\-versus\-block equivalence\. Dream\-7B collapses somewhat less than LLaDA\-8B under ordered decoding but has lower absolute accuracy throughout; the replication is qualitative, not numerical\.

#### MATH\-500\.

Three cells \(pure, semi\-AR block 32, gatedw=16w\{=\}16\) atL=512L\{=\}512,n=250n\{=\}250paired\. Accuracies0\.188/0\.356/0\.3400\.188/0\.356/0\.340; collapse13\.6%/0\.0%/0\.0%13\.6\\%/0\.0\\%/0\.0\\%; truncation0%0\\%;\\\\backslashboxeddetection65\.6%65\.6\\%for pure versus∼\\sim80%80\\%for the ordered decoders, itself a signal of degraded generation under pure decoding\. Commit\-order statistics on non\-collapsed outputs \(a post\-hoc analysis\): answertnorm∗t^\{\*\}\_\{\\text\{norm\}\}0\.2750\.275\(pure\) versus0\.9600\.960and0\.9500\.950\(semi\-AR, gated\), with reasoningτ\\taunear0\.50\.5in all three\.

## Appendix DAdaptive window schedules

The low\-NFE deficit of §[6\.2](https://arxiv.org/html/2608.05687#S6.SS2)admits a natural mechanistic explanation: if the eligible set is smaller than the number of tokens the schedule must commit at each step, the sampler is forced to finalize adjacent positions before their neighbors resolve\. That explanation implies a remedy—let the window track the demand\. Writingmtm\_\{t\}for the masked tokens remaining andsts\_\{t\}for the steps remaining, we setwt=max⁡\(wmin,⌈c⋅mt/st⌉\)w\_\{t\}=\\max\(w\_\{\\min\},\\lceil c\\cdot m\_\{t\}/s\_\{t\}\\rceil\), which is wide early and narrows as decoding proceeds\. At512512steps the demand is≈1\\approx 1, so the schedule degenerates to a fixed small window; we verified this exactly, with\(c=1,wmin=1\)\(c\{=\}1,w\_\{\\min\}\{=\}1\)reproducing fixedw=1w\{=\}1token\-for\-token\.

Across\(c,wmin\)∈\{\(2,8\),\(4,8\),\(4,16\),\(8,16\)\}\(c,w\_\{\\min\}\)\\in\\\{\(2,8\),\(4,8\),\(4,16\),\(8,16\)\\\}and steps∈\{512,256,128,64\}\\in\\\{512,256,128,64\\\}\(GSM8K,n=250n\{=\}250paired\), the schedule preserves full\-refinement accuracy \(0\.8360\.836at 512 steps, within1\.6​pp1\.6\\,\\mathrm\{pp\}of fixedw=1w\{=\}1\) but buys nothing at reduced budgets: its best NFE\-128 cell reaches0\.7080\.708against0\.7160\.716for fixedw=16w\{=\}16\(McNemarp=0\.80p\{=\}0\.80\), and its best NFE\-64 cell reaches0\.3800\.380, below unconstrained decoding \(p=0\.001p\{=\}0\.001\)\. We had registered the opposite prediction and report the miss\.

Two details make this negative result informative rather than merely disappointing\. First, degeneration does not fall \(0\.200\.20–0\.240\.24, against0\.200\.20for fixedw=16w\{=\}16\), so the starvation account of the damage is wrong: widening the window does not repair the corrupted tokens\. Second, conditioning on non\-collapsed outputs, the schedule reaches0\.3610\.361at NFE 64—the same ceiling as every other decoder \(≈\\approx0\.300\.30\)\. The obstacle at eight tokens per step is thus the density of commitment itself, not the space available for it, which is why a spatial remedy leaves it untouched\.

## Appendix EExtended discussion

#### Unfaithful chain\-of\-thought, made legible\.

In autoregressive models, post\-hoc rationalization must be inferred: the answer appears after the reasoning, so pre\-commitment is detected with probes, steering, or CoT perturbation\(Turpinet al\.,[2023](https://arxiv.org/html/2608.05687#bib.bib3); Lanham and others,[2023](https://arxiv.org/html/2608.05687#bib.bib4); Jianget al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib21); Parekh,[2026](https://arxiv.org/html/2608.05687#bib.bib22)\)\. Pure diffusion decoding removes the inference step twice over\. The commitment log*is*the ground truth of causal order, and the mechanism is stronger than in the AR case: the committed answer conditions subsequent reasoning not through hidden state but as literal tokens in bidirectional context\. Answer\-conditioned rationale generation, which AR studies construct artificially to stress\-test faithfulness\(Jianget al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib21)\), is pure decoding’s default operating regime—making unfaithful CoT structurally likely and, in the same stroke, directly observable\. We expect this legibility to be useful beyond the present paper\.

#### Three faces of one failure\.

The scale argument of §[7](https://arxiv.org/html/2608.05687#S7)sorts our failure modes along three axes of the same commitment policy:*collapse*in space, where distant positions are reachable before any context exists;*backfill*in order, where the conclusion becomes context for its own derivation; and*token corruption*in temporal density, where neighbours are finalized before their mutual context resolves\. None is a deficit of the model’s beliefs—pressure, answer previews, and local order are near\-identical across decoders—and each is switched on or off by what the sampler is permitted to do with those beliefs\.

#### Semi\-AR as overprescription\.

The scale argument of §[7](https://arxiv.org/html/2608.05687#S7)reframes semi\-AR decoding, quietly shipped as the default configuration for exactly these benchmarks, as an overprescription that happened to contain the active ingredient: its blocks restrict reachability, and §[6\.1](https://arxiv.org/html/2608.05687#S6.SS1)shows the restriction, not the block structure, does all the work\. We also note that the crossover of §[6\.2](https://arxiv.org/html/2608.05687#S6.SS2)is an empirical boundary—we offer no theory of*why*four tokens per step is where order stops paying\.

#### A gradient of remedies\.

The available interventions sort by depth\. Sampling temperature does nothing—the collapse set is per\-problem invariant \(Jaccard0\.9960\.996\)\. Prompting helps partially \(88%→58%88\\%\\to 58\\%with official few\-shot exemplars\)\. Retraining, the EOS\-overflow literature’s prescription, targets pressure, which we find near\-constant across the decoders that do and do not collapse\. Making commitments reversible\(Wanget al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib28); Yuet al\.,[2026b](https://arxiv.org/html/2608.05687#bib.bib26)\)addresses the same root cause but, in its strongest current form, requires post\-training before revision helps rather than hurts; prevention and revision are orthogonal and plausibly composable\. Constraining reachability removes the pathology almost entirely \(1\.8%1\.8\\%–8\.4%8\.4\\%\) at zero training cost\.

#### Reconciliation withYuet al\.\([2026a](https://arxiv.org/html/2608.05687#bib.bib31)\)\.

Yuet al\.\([2026a](https://arxiv.org/html/2608.05687#bib.bib31)\)find masked dLLMs*robust*to answer\-first prompting where autoregressive models are not, and attribute this to confidence\-ordered sampling deferring hard answer tokens until the surrounding reasoning has settled\. Their configuration overlaps ours almost exactly—LLaDA\-8B\-Instruct, low\-confidence remasking, temperature0, block equal to generation length—so the tension deserves a plain statement\. Their own timings dissolve much of it: answer tokens at their two easiest difficulty levels are exposed at steps 10 and 13 of 256, relatively earlier than the1515–24%24\\%we measure, and only the two hardest are deferred; the deferral is conditional on the answer being genuinely uncertain, and the quantity they defend is accuracy under a*reordered prompt*rather than across decoders\. Their analysis of breakdown conditions corroborates two of our findings from the other side—a longer canvas degrades reasoning, and similar\-complexity tokens are committed early and cannot then be repaired\. One discrepancy remains: on their benchmark forced left\-to\-right underperforms confidence\-based decoding, whereasw=1w\{=\}1is best in our sweep\. Their task pairs a long distractor passage with a structured output template and ours is free\-form arithmetic; we leave the task dependence open\.

#### Outlook\.

The flip of the optimal window with NFE invites*adaptive*schedulesw​\(t\)w\(t\)that widen as the refinement budget shrinks; the same knob would interpolate between the left\-to\-right RL policy ofNiet al\.\([2026](https://arxiv.org/html/2608.05687#bib.bib18)\)and unconstrained exploration\. The collapse detector implicit in our logs invites semantic rescue—injecting a continuation cue when termination is committing prematurely\(Jinet al\.,[2025](https://arxiv.org/html/2608.05687#bib.bib9)\)—in a setting where, unlike in AR models, the moment of premature commitment is directly observable\. And if termination and answer\-preview features can be located in representation space\(Wanget al\.,[2026a](https://arxiv.org/html/2608.05687#bib.bib19)\), the gate could move from positions to features\.