CORA-Diff: Confidence-Oriented Residual Acceptance for Efficient Diffusion Language Model Inference

# CORA-Diff: Confidence-Oriented Residual Acceptance for Efficient Diffusion Language Model Inference
Source: [https://arxiv.org/html/2608.11235](https://arxiv.org/html/2608.11235)
###### Abstract

Diffusion language models \(DLMs\) update many tokens in parallel, yet practical decoders often use a fixed denoising horizon\. Many predictions stabilize early, but blockwise decoding continues until the remaining positions are resolved, leaving repeated dense forward passes\. Existing accelerators reduce this redundancy but often rely on learned filters, modified scores, dependency models, or cache\-specific mechanisms\. We instead ask whether native trajectory signals alone can identify residual positions likely to match the deterministic dense endpoint\. We proposeCORA\-Diff, a training\-free method that preserves the original transfer rule and applies confidence\-and\-persistence gating only to positions that rule leaves unresolved\. Accepted tokens remain visible as context, and the block terminates once all positions are resolved\. This requires no backbone change, learned acceptance model, or logit modification\. We analyze reliability through agreement with the fixed\-horizon dense endpoint\. Our theory explains why high\-confidence, persistent predictions are more likely to match this endpoint, and paired post\-intervention trajectories provide direct empirical support\. We select one operating point on a separate GSM8K calibration subset and freeze it for all subsequent evaluations\. Under a matched Learn2PD\-style LLaDA protocol, CORA\-Diff has the lowest measured runtime in all eight task–length settings\. Task scores match or exceed dense decoding in five settings, and the largest observed drop is 1\.22 points\. Its incremental speedups over EOS\-aware dense decoding are2\.70×2\.70\\timesand3\.32×3\.32\\timeson GSM8K and HumanEval\. It also reaches13\.14×13\.14\\timesunder the fixed\-horizon 1024/1024 mechanism\-isolation protocol and transfers to Dream without retuning at3\.18×3\.18\\times–3\.53×3\.53\\times\. These results demonstrate that native confidence and persistence are sufficient in practice for reliable residual acceptance, allowing a simple training\-free gate to remove substantial repeated denoising computation while preserving task quality\.

Code—https://github\.com/wyffffff/cora\-diff\-llada

## 1Introduction

Autoregressive language models generate tokens sequentially, whereas diffusion language models \(DLMs\) can update many positions in parallel\(Austinet al\.[2021a](https://arxiv.org/html/2608.11235#bib.bib9); Louet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib14); Shiet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib15); Sahooet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib16)\)\. This parallelism is promising, but it does not guarantee fast inference\. Many practical DLM decoders use a fixed denoising horizon and execute one dense Transformer pass per step\(Nieet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib20); Yeet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib22)\)\. In blockwise variants, this horizon is assigned to each generation block\(Nieet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib20); Arriolaet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib19)\)\. These passes may continue after many predictions have stabilized\. Because every executed pass remains dense, accepting individual tokens reduces latency only when the original transfer rule and early acceptance jointly resolve the active block\. The central challenge is therefore to determine when positions left unresolved by the original rule are reliable enough to accept, so that the active block can finish and skip its remaining dense passes\.

Prior work confirms that fixed\-horizon decoding can waste computation\. Prophet observes*early answer convergence*, and Learn2PD shows that some tokens match the final output well before decoding ends\(Liet al\.[2026a](https://arxiv.org/html/2608.11235#bib.bib39); Baoet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib24)\)\. Existing accelerators use learned acceptance\(Baoet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib24); Chenet al\.[2026c](https://arxiv.org/html/2608.11235#bib.bib27)\), logit modification\(Wanget al\.[2026](https://arxiv.org/html/2608.11235#bib.bib28)\), dependency\-aware or adaptive schedules\(Luoet al\.[2026a](https://arxiv.org/html/2608.11235#bib.bib44); Kimet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib68); Ringelet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib45); Weiet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib69)\), cache reuse or focused computation\(Wuet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib35); Liuet al\.[2026b](https://arxiv.org/html/2608.11235#bib.bib36); Huet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib37); Lianget al\.[2026](https://arxiv.org/html/2608.11235#bib.bib38)\), and speculative checking\(Panet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib42)\)\. These routes are effective, but they often require learned components, modified decision scores, explicit dependency models, or specialized system support\. We ask a complementary question: does the native denoising trajectory already contain enough evidence to accept unresolved positions without extra training, backbone changes, or logit modification?

Early acceptance faces two immediate failure modes: the current prediction may be weakly supported, or it may change as denoising evolves\. These failure modes suggest two complementary signals already available in the native denoising trajectory: top\-1 confidence measures instantaneous support, while cross\-step persistence measures trajectory stability\. Both are computed from outputs already produced at each executed step, requiring no auxiliary model or extra forward pass\. We test this hypothesis by comparing residual\-position predictions with the fixed\-horizon dense endpoint and stratifying disagreement by confidence\.

![Refer to caption](https://arxiv.org/html/2608.11235v1/x1.png)Figure 1:Dense\-trace diagnostic for early acceptance of unresolved tokens\. On dense LLaDA traces from all 1,319 GSM8K and 164 HumanEval test prompts, token disagreement with the full\-horizon dense endpoint generally decreases with persistence within fixed top\-1 confidence ranges\. Bands and error bars show 95% confidence intervals obtained by resampling prompts, marker area indicates the number of candidate\-token states, andm≥6m\\geq 6is pooled\. The overall decline shows that persistence provides reliability information beyond confidence alone\.Figure[1](https://arxiv.org/html/2608.11235#S1.F1)shows that, within fixed confidence ranges, persistent predictions are less likely to disagree with the dense endpoint on unperturbed LLaDA traces\. Prompt\-level bootstrap intervals account for dependence among states from the same prompt\. Although individual bins contain local reversals, both tasks show the same overall pattern: persistence adds reliability information beyond confidence\. Because committing tokens early can change later predictions, we also test on actual CORA\-Diff runs whether persistent predictions remain more likely to match the paired dense endpoint\.

Motivated by this observation, we proposeCORA\-Diff\(Confidence\-OrientedResidualAcceptance for Diffusion Language Models\), a training\-free residual acceptance decoder\. CORA\-Diff preserves the original transfer rule and applies its gate only to positions that rule leaves unresolved\. A position is accepted only when its top\-1 prediction is both confident and persistent\. Positions fixed by the original rule or accepted by CORA\-Diff remain visible as context\. Once the two rules jointly resolve the block, decoding stops and the remaining dense passes are skipped\. Thus, CORA\-Diff reduces the number of executed steps without an auxiliary verifier, backbone changes, or logit modification\.

We evaluate reliability by comparing early accepted tokens with the fixed\-horizon dense endpoint\. Our analysis explains why high confidence and persistent predictions favor endpoint agreement, and paired post\-intervention trajectories test this relationship on actual CORA\-Diff states\. We select thresholds on an independent calibration set, characterize this selection with a finite\-sample bound, and then measure task quality and block\-level computation savings on held\-out benchmarks\.

We select\(δp,m\)=\(0\.65,1\)\(\\delta\_\{p\},m\)=\(0\.65,1\)on a separate 1,000\-prompt GSM8K calibration subset and freeze it for all reported test and cross\-backbone transfer experiments\. We evaluate LLaDA\-8B\-Instruct on GSM8K, MATH, HumanEval, and MBPP, and test transfer to Dream\. CORA\-Diff has the lowest measured runtime in all eight matched LLaDA settings; task scores match or exceed dense decoding in five settings, and the largest decrease is 1\.22 points\. Under a shared EOS\-aware controller implemented with end\-of\-text prediction \(EoTP\), decoding terminates only after a committed end\-of\-sequence \(EOS\) token\. Its incremental deployment speedups are2\.70×2\.70\\timesand3\.32×3\.32\\timesover EOS\-aware dense decoding on GSM8K and HumanEval\. The fixed\-horizon 1024/1024 mechanism\-isolation protocol gives the larger13\.14×13\.14\\timesresult\. With the same thresholds and no retuning, CORA\-Diff reaches3\.18×3\.18\\times–3\.53×3\.53\\timesspeedup on Dream, with task\-score changes of at most 0\.006\.

Our contributions are:

- •We proposeCORA\-Diff, a training\-free residual acceptance method without logit modification\. It applies confidence\-and\-persistence gating only to positions left unresolved by the original transfer rule\.
- •We formalize early acceptance through dense\-endpoint disagreement and give a margin\-based sufficient condition for accepted\-token agreement\. Under an explicit at\-risk persistence–drift separation assumption, we derive a conditional drift\-tail bound and analyze the actual calibration selector\.
- •We show that this lightweight rule enables block\-level early termination\. It achieves2\.70×2\.70\\times–3\.32×3\.32\\timesincremental speedups over EOS\-aware dense decoding, reaches13\.14×13\.14\\timesin fixed\-horizon mechanism isolation, and transfers to Dream without retuning\.

## 2Related Work

#### Diffusion language models\.

Diffusion language models generate text by iteratively denoising or unmasking corrupted sequences\. Prior work studies discrete corruption, continuous diffusion over embeddings, and masked or score\-based objectives\(Austinet al\.[2021a](https://arxiv.org/html/2608.11235#bib.bib9); Campbellet al\.[2022](https://arxiv.org/html/2608.11235#bib.bib11); Liet al\.[2022](https://arxiv.org/html/2608.11235#bib.bib12); Louet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib14); Shiet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib15); Sahooet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib16); Zhenget al\.[2025](https://arxiv.org/html/2608.11235#bib.bib17); Ouet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib18)\)\. Large\-scale examples include LLaDA, DiffuLLaMA, and Dream\(Nieet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib20); Gonget al\.[2025](https://arxiv.org/html/2608.11235#bib.bib21); Yeet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib22)\)\. Block Diffusion combines autoregressive dependencies across blocks with diffusion refinement within each block\(Arriolaet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib19)\)\. CORA\-Diff leaves these modeling choices and the pretrained backbone unchanged and targets repeated work during inference\.

#### Acceptance and step reduction\.

DLM accelerators use different reliability signals and therefore stop at different operating points\(Kanget al\.[2026](https://arxiv.org/html/2608.11235#bib.bib43)\)\. The four baselines in our matched comparison span the closest routes: Prophet uses early answer convergence, KLASS uses distributional stability, DAPD uses dependency\-aware decoding, and Learn2PD trains a lightweight filter for endpoint agreement\(Liet al\.[2026a](https://arxiv.org/html/2608.11235#bib.bib39); Kimet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib26),[2026](https://arxiv.org/html/2608.11235#bib.bib68); Baoet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib24)\)\. Other methods adapt block sizes, confidence schedules, or token clusters\(Luet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib40); Mohamedet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib41); Luoet al\.[2026b](https://arxiv.org/html/2608.11235#bib.bib32)\)\. Learned policies and trace\-based rules further use model training, self\-distillation, or decoding histories\(Chenet al\.[2026b](https://arxiv.org/html/2608.11235#bib.bib29),[c](https://arxiv.org/html/2608.11235#bib.bib27); Wanget al\.[2026](https://arxiv.org/html/2608.11235#bib.bib28); Sunet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib30); Liet al\.[2026b](https://arxiv.org/html/2608.11235#bib.bib31)\)\. Dependency\-aware methods explicitly model interactions among masked positions\(Luoet al\.[2026a](https://arxiv.org/html/2608.11235#bib.bib44); Ringelet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib45); Sahinet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib33)\)\. CORA\-Diff targets block completion rather than token acceptance alone: it clears the last unresolved positions so that the block can skip remaining dense passes\.

#### Per\-step and system acceleration\.

An orthogonal line reduces the cost of each executed step through KV reuse, focused computation, speculative verification, or expert offloading\(Wuet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib35); Liuet al\.[2026b](https://arxiv.org/html/2608.11235#bib.bib36); Huet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib37); Lianget al\.[2026](https://arxiv.org/html/2608.11235#bib.bib38); Panet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib42); Chenet al\.[2026a](https://arxiv.org/html/2608.11235#bib.bib34)\)\. WeDLM changes the attention structure and reorders generation to enable prefix KV caching and streaming decoding\(Liuet al\.[2026a](https://arxiv.org/html/2608.11235#bib.bib71)\)\. These methods reduce per\-step or system cost, whereas CORA\-Diff reduces the number of executed dense steps; the cache experiment tests their compatibility\. This distinction also separates CORA\-Diff from broader adaptive\-computation methods that change layer, width, or token\-level execution\(Goyalet al\.[2020](https://arxiv.org/html/2608.11235#bib.bib51); Houet al\.[2020](https://arxiv.org/html/2608.11235#bib.bib52); Elhoushiet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib53); Raposoet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib54); Devvritet al\.[2024](https://arxiv.org/html/2608.11235#bib.bib55)\)\.

## 3Method

We proposeCORA\-Diff\(Confidence\-OrientedResidualAcceptance for Diffusion Language Models\), a training\-free DLM decoder\. It freezes the backbone and retains dense Transformer execution at every step that is run\. It reduces the number of such steps by accepting unresolved positions whose top\-1 predictions are both confident and persistent\. Figure[2](https://arxiv.org/html/2608.11235#S3.F2)summarizes the procedure\. Accepted tokens remain visible as context\. When no unresolved position remains, CORA\-Diff terminates the block and skips the remaining forward passes\.

![Refer to caption](https://arxiv.org/html/2608.11235v1/x2.png)Figure 2:Overview of CORA\-Diff\. Standard decoding executes a fixed denoising horizon for each block\. At each step, the original transfer rule first fixes a subset of positions\. CORA\-Diff applies its residual gate only to the remaining positions and accepts a token when it satisfies bothci\(s\)≥δpc\_\{i\}^\{\(s\)\}\\geq\\delta\_\{p\}andmi\(s\)≥mm\_\{i\}^\{\(s\)\}\\geq m\. Tokens fixed by either rule remain visible as context\. Once no unresolved position remains, the block terminates and skips the remaining dense forward passes\.### 3\.1Diffusion Decoding Setup

Let𝐱\(s\)=\(x1\(s\),…,xn\(s\)\)\\mathbf\{x\}^\{\(s\)\}=\(x\_\{1\}^\{\(s\)\},\\dots,x\_\{n\}^\{\(s\)\}\)be the partially denoised sequence at stepss\. Let𝒰\(s\)\\mathcal\{U\}^\{\(s\)\}be the set of unresolved positions\. For each unresolved tokeni∈𝒰\(s\)i\\in\\mathcal\{U\}^\{\(s\)\}, the diffusion language model produces logitsℓi\(s\)\\boldsymbol\{\\ell\}\_\{i\}^\{\(s\)\}and token distribution𝐩i\(s\)=softmax⁡\(ℓi\(s\)\)\\mathbf\{p\}\_\{i\}^\{\(s\)\}=\\operatorname\{softmax\}\(\\boldsymbol\{\\ell\}\_\{i\}^\{\(s\)\}\)\. The current prediction and its confidence are

x^i\(s\)=arg⁡maxv⁡pi,v\(s\),ci\(s\)=maxv⁡pi,v\(s\)\.\\hat\{x\}\_\{i\}^\{\(s\)\}=\\arg\\max\_\{v\}p\_\{i,v\}^\{\(s\)\},\\qquad c\_\{i\}^\{\(s\)\}=\\max\_\{v\}p\_\{i,v\}^\{\(s\)\}\.\(1\)
In the blockwise masked\-diffusion decoding setup used by LLaDA, generation tokens are partitioned into blocks and decoded one block at a time\. Each block has a fixed denoising horizon\. At each step, the model predicts all currently masked positions, after which the original transfer rule fixes a subset by confidence or remasking\. This conservative schedule can keep refining already\-stable predictions\. CORA\-Diff adds training\-free early acceptance on top of the original schedule\.

### 3\.2Confidence\-Oriented Residual Acceptance

At temperature zero, the trajectory and full\-horizon endpoint are deterministic for each prompt\. LetQ∼𝒟Q\\sim\\mathcal\{D\}and letYQ⋆Y\_\{Q\}^\{\\star\}be the output of the original dense decoder\. At the prompt level, probabilities are induced byQ∼𝒟Q\\sim\\mathcal\{D\}; the state\-level analysis in Section[3\.3](https://arxiv.org/html/2608.11235#S3.SS3)additionally draws a token–step state from a fixed offline analysis measure\. We evaluate early decisions by population disagreement withYQ⋆Y\_\{Q\}^\{\\star\}, which measures deviation from dense decoding rather than task correctness\.

CORA\-Diff uses top\-1 confidence and cross\-step prediction persistence, both available from the current decoding trajectory\.

For each unresolved token, we maintain a persistence counter:

mi\(s\)=\{mi\(s−1\)\+1,if​x^i\(s\)=x^i\(s−1\),0,otherwise\.m\_\{i\}^\{\(s\)\}=\\begin\{cases\}m\_\{i\}^\{\(s\-1\)\}\+1,&\\text\{if \}\\hat\{x\}\_\{i\}^\{\(s\)\}=\\hat\{x\}\_\{i\}^\{\(s\-1\)\},\\\\ 0,&\\text\{otherwise\}\.\\end\{cases\}\(2\)A largermi\(s\)m\_\{i\}^\{\(s\)\}means that the same prediction has persisted for more consecutive denoising steps\. At a position’s first executed step the counter is zero\. Thusm=0m=0is confidence\-only, whereasm=1m=1requires the same top\-1 prediction on two consecutive executed steps; skipped steps do not update it\.

CORA\-Diff accepts tokeniiat stepssif it is both confident and persistent:

ai\(s\)=𝕀​\[ci\(s\)≥δp∧mi\(s\)≥m\],a\_\{i\}^\{\(s\)\}=\\mathbb\{I\}\\left\[c\_\{i\}^\{\(s\)\}\\geq\\delta\_\{p\}\\;\\land\\;m\_\{i\}^\{\(s\)\}\\geq m\\right\],\(3\)whereδp\\delta\_\{p\}is the confidence threshold andmmis the required persistence window\. Let𝒯\(s\)⊆𝒰\(s\)\\mathcal\{T\}^\{\(s\)\}\\subseteq\\mathcal\{U\}^\{\(s\)\}be the positions fixed by the original transfer rule at stepss\. The residual gate is applied only to the remaining positions; let𝒜\(s\)\\mathcal\{A\}^\{\(s\)\}denote the positions it accepts\. Each tokeni∈𝒜\(s\)i\\in\\mathcal\{A\}^\{\(s\)\}is fixed to its current prediction, and the unresolved set is updated by both rules:

xi\(s\+1\)\\displaystyle x\_\{i\}^\{\(s\+1\)\}←x^i\(s\)\\displaystyle\\leftarrow\\hat\{x\}\_\{i\}^\{\(s\)\}\(i∈𝒜\(s\)\),\\displaystyle\(i\\in\\mathcal\{A\}^\{\(s\)\}\),\(4\)𝒰\(s\+1\)\\displaystyle\\mathcal\{U\}^\{\(s\+1\)\}=𝒰\(s\)∖\(𝒯\(s\)∪𝒜\(s\)\)\.\\displaystyle=\\mathcal\{U\}^\{\(s\)\}\\setminus\\left\(\\mathcal\{T\}^\{\(s\)\}\\cup\\mathcal\{A\}^\{\(s\)\}\\right\)\.Accepted tokens remain visible as context for unresolved positions\. Thus, CORA\-Diff does not discard accepted tokens\. It only prevents them from being denoised again\.

The persistence condition prevents a one\-step confidence spike from triggering acceptance\.

#### Why confidence is informative\.

Letv=x^i\(s\)v=\\hat\{x\}\_\{i\}^\{\(s\)\}andγi\(s\)=ℓi,v\(s\)−maxu≠v⁡ℓi,u\(s\)\\gamma\_\{i\}^\{\(s\)\}=\\ell\_\{i,v\}^\{\(s\)\}\-\\max\_\{u\\neq v\}\\ell\_\{i,u\}^\{\(s\)\}be its current logit margin\. LetsQ,i⋆s\_\{Q,i\}^\{\\star\}be the pass whose original transfer rule permanently commits positionii\. This rule commits the current top\-1 token, soYQ,i⋆=arg⁡maxu⁡ℓQ,i,u⋆Y\_\{Q,i\}^\{\\star\}=\\arg\\max\_\{u\}\\ell\_\{Q,i,u\}^\{\\star\}, whereℓQ,i⋆\\boldsymbol\{\\ell\}\_\{Q,i\}^\{\\star\}denotes the pre\-transfer logits\. Permanent means no later remask or modification\. If the position remains unresolved through the horizon, these are the final\-pass logits and their deterministically tie\-broken top\-1 token\.

###### Proposition 1\(Endpoint\-preservation condition\)\.

If

‖ℓQ,i⋆−ℓi\(s\)‖∞<γi\(s\)2,\\left\\\|\\boldsymbol\{\\ell\}\_\{Q,i\}^\{\\star\}\-\\boldsymbol\{\\ell\}\_\{i\}^\{\(s\)\}\\right\\\|\_\{\\infty\}<\\frac\{\\gamma\_\{i\}^\{\(s\)\}\}\{2\},\(5\)thenx^i\(s\)=YQ,i⋆\\hat\{x\}\_\{i\}^\{\(s\)\}=Y\_\{Q,i\}^\{\\star\}\. Moreover, ifci\(s\)\>1/2c\_\{i\}^\{\(s\)\}\>1/2, thenγi\(s\)≥log⁡\(ci\(s\)/\(1−ci\(s\)\)\)\.\\gamma\_\{i\}^\{\(s\)\}\\geq\\log\\\!\\bigl\(c\_\{i\}^\{\(s\)\}/\(1\-c\_\{i\}^\{\(s\)\}\)\\bigr\)\.

###### Proof\.

Let𝚫=ℓQ,i⋆−ℓi\(s\)\\boldsymbol\{\\Delta\}=\\boldsymbol\{\\ell\}\_\{Q,i\}^\{\\star\}\-\\boldsymbol\{\\ell\}\_\{i\}^\{\(s\)\}\. For everyu≠vu\\neq v,

ℓQ,i,v⋆−ℓQ,i,u⋆\\displaystyle\\ell\_\{Q,i,v\}^\{\\star\}\-\\ell\_\{Q,i,u\}^\{\\star\}=ℓi,v\(s\)−ℓi,u\(s\)\+Δv−Δu\\displaystyle=\\ell\_\{i,v\}^\{\(s\)\}\-\\ell\_\{i,u\}^\{\(s\)\}\+\\Delta\_\{v\}\-\\Delta\_\{u\}≥γi\(s\)−\|Δv\|−\|Δu\|\\displaystyle\\geq\\gamma\_\{i\}^\{\(s\)\}\-\|\\Delta\_\{v\}\|\-\|\\Delta\_\{u\}\|≥γi\(s\)−2​‖𝚫‖∞\>0\.\\displaystyle\\geq\\gamma\_\{i\}^\{\(s\)\}\-2\\\|\\boldsymbol\{\\Delta\}\\\|\_\{\\infty\}\>0\.\(6\)Hencevvis the unique dense\-reference top\-1 token andv=YQ,i⋆v=Y\_\{Q,i\}^\{\\star\}\. Ifu2u\_\{2\}is the current runner\-up, the softmax ratio givesγi\(s\)=log⁡\(pi,v\(s\)/pi,u2\(s\)\)\\gamma\_\{i\}^\{\(s\)\}=\\log\(p\_\{i,v\}^\{\(s\)\}/p\_\{i,u\_\{2\}\}^\{\(s\)\}\)\. Sincepi,u2\(s\)≤1−ci\(s\)p\_\{i,u\_\{2\}\}^\{\(s\)\}\\leq 1\-c\_\{i\}^\{\(s\)\}, the stated lower bound follows\. ∎

Although the reference logits are unavailable online, the condition formalizes why high confidence creates a wider top\-1 stability margin\. Persistence supplies an observable trajectory signal for whether that margin is likely to be preserved; dense\-trace diagnostics and paired post\-intervention analysis test this mechanism empirically\.

### 3\.3Population Disagreement and Calibration

Leth=\(δp,m\)h=\(\\delta\_\{p\},m\)denote a CORA\-Diff configuration\. For promptQQ, let𝒜Q​\(h\)\\mathcal\{A\}\_\{Q\}\(h\)be the positions accepted by the residual gate, letsihs\_\{i\}^\{h\}be the acceptance step for positionii, and letY~Q,ih\\widetilde\{Y\}\_\{Q,i\}^\{h\}be its accepted token\. We define prompt\-level accepted\-token disagreement as

LQacc​\(h\)=1max⁡\{1,\|𝒜Q​\(h\)\|\}​∑i∈𝒜Q​\(h\)𝕀​\[Y~Q,ih≠YQ,i⋆\]\.L\_\{Q\}^\{\\mathrm\{acc\}\}\(h\)=\\frac\{1\}\{\\max\\\{1,\|\\mathcal\{A\}\_\{Q\}\(h\)\|\\\}\}\\sum\_\{i\\in\\mathcal\{A\}\_\{Q\}\(h\)\}\\mathbb\{I\}\[\\widetilde\{Y\}\_\{Q,i\}^\{h\}\\neq Y\_\{Q,i\}^\{\\star\}\]\.\(7\)We set this loss to zero when no position is accepted\. Its population value is

R𝒟acc​\(h\)=𝔼Q∼𝒟​\[LQacc​\(h\)\]\.R\_\{\\mathcal\{D\}\}^\{\\mathrm\{acc\}\}\(h\)=\\mathbb\{E\}\_\{Q\\sim\\mathcal\{D\}\}\[L\_\{Q\}^\{\\mathrm\{acc\}\}\(h\)\]\.\(8\)This quantity measures the reliability of the acceptance decisions themselves\.

#### How persistence controls drift\-tail probability\.

Fixh=\(δp,m\)h=\(\\delta\_\{p\},m\); the trajectory and all state events below depend onhh, with superscripts omitted\. To preserve the prompt\-balanced weighting in Eq\. \([7](https://arxiv.org/html/2608.11235#S3.E7)\), letνQh\\nu\_\{Q\}^\{h\}be an offline measure whose first\-hit restriction is uniform over accepted positions within each prompt; the supplement gives its canonical definition\. Probabilities below drawQ∼𝒟Q\\sim\\mathcal\{D\}and a state fromνQh\\nu\_\{Q\}^\{h\}\. Letℛi,s\\mathcal\{R\}\_\{i,s\}mean thatiiremains unresolved after the original rule atssand was not accepted earlier, and let𝒢i,s=\{ci\(s\)≥δp\}\\mathcal\{G\}\_\{i,s\}=\\\{c\_\{i\}^\{\(s\)\}\\geq\\delta\_\{p\}\\\}\. The observable stratumZi,sZ\_\{i,s\}contains only confidence, normalized time, block, and optional dataset/backbone bins\. DefineDQ,i\(s\)=‖ℓQ,i⋆−ℓi\(s\)‖∞D\_\{Q,i\}^\{\(s\)\}=\\\|\\boldsymbol\{\\ell\}\_\{Q,i\}^\{\\star\}\-\\boldsymbol\{\\ell\}\_\{i\}^\{\(s\)\}\\\|\_\{\\infty\},g​\(δp\)=12​log⁡δp1−δpg\(\\delta\_\{p\}\)=\\frac\{1\}\{2\}\\log\\frac\{\\delta\_\{p\}\}\{1\-\\delta\_\{p\}\}, andℬi,s=\{DQ,i\(s\)≥g​\(δp\)\}\\mathcal\{B\}\_\{i,s\}=\\\{D\_\{Q,i\}^\{\(s\)\}\\geq g\(\\delta\_\{p\}\)\\\}\. Forr≥1r\\geq 1, defineℋi,s\(r\)=\{x^i\(s−r\+1\)=x^i\(s−r\)\}\\mathcal\{H\}\_\{i,s\}^\{\(r\)\}=\\\{\\hat\{x\}\_\{i\}^\{\(s\-r\+1\)\}=\\hat\{x\}\_\{i\}^\{\(s\-r\)\}\\\}andℱi,s\(r\)=∩j=1rℋi,s\(j\)\\mathcal\{F\}\_\{i,s\}^\{\(r\)\}=\\cap\_\{j=1\}^\{r\}\\mathcal\{H\}\_\{i,s\}^\{\(j\)\}, withℱi,s\(0\)=Ω\\mathcal\{F\}\_\{i,s\}^\{\(0\)\}=\\Omega\. For compactness, set𝒞i,s,z\(r\)=ℱi,s\(r\)∩ℛi,s∩𝒢i,s∩\{Zi,s=z\}\\mathcal\{C\}\_\{i,s,z\}^\{\(r\)\}=\\mathcal\{F\}\_\{i,s\}^\{\(r\)\}\\cap\\mathcal\{R\}\_\{i,s\}\\cap\\mathcal\{G\}\_\{i,s\}\\cap\\\{Z\_\{i,s\}=z\\\}\.

###### Assumption 1\(Conditional persistence–drift separation\)\.

Letqz,r\+q\_\{z,r\}^\{\+\}andqz,r−q\_\{z,r\}^\{\-\}be the conditional probabilities ofℋi,s\(r\)\\mathcal\{H\}\_\{i,s\}^\{\(r\)\}underℬi,s\\mathcal\{B\}\_\{i,s\}andℬi,sc\\mathcal\{B\}\_\{i,s\}^\{c\}, respectively, given𝒞i,s,z\(r−1\)\\mathcal\{C\}\_\{i,s,z\}^\{\(r\-1\)\}\. For every supportedz,rz,rwithqz,r−\>0q\_\{z,r\}^\{\-\}\>0, someλz,r\>0\\lambda\_\{z,r\}\>0satisfies

qz,r\+qz,r−≤e−λz,r\.\\frac\{q\_\{z,r\}^\{\+\}\}\{q\_\{z,r\}^\{\-\}\}\\leq e^\{\-\\lambda\_\{z,r\}\}\.\(9\)

###### Proposition 2\(Persistence\-conditioned drift\-tail bound\)\.

Letπz=Pr⁡\(ℬi,s∣𝒞i,s,z\(0\)\)\\pi\_\{z\}=\\Pr\(\\mathcal\{B\}\_\{i,s\}\\mid\\mathcal\{C\}\_\{i,s,z\}^\{\(0\)\}\)andΛz​\(m\)=∑r=1mλz,r\\Lambda\_\{z\}\(m\)=\\sum\_\{r=1\}^\{m\}\\lambda\_\{z,r\}\. Under Assumption[1](https://arxiv.org/html/2608.11235#Thmassumption1)andδp\>1/2\\delta\_\{p\}\>1/2,

Pr⁡\(x^i\(s\)≠YQ,i⋆∣𝒞i,s,z\(m\)\)\\displaystyle\\Pr\(\\hat\{x\}\_\{i\}^\{\(s\)\}\\neq Y\_\{Q,i\}^\{\\star\}\\mid\\mathcal\{C\}\_\{i,s,z\}^\{\(m\)\}\)≤Pr⁡\(ℬi,s∣𝒞i,s,z\(m\)\)\\displaystyle\\leq\\Pr\(\\mathcal\{B\}\_\{i,s\}\\mid\\mathcal\{C\}\_\{i,s,z\}^\{\(m\)\}\)\(10\)≤πz​e−Λz​\(m\)1−πz\+πz​e−Λz​\(m\)\.\\displaystyle\\leq\\frac\{\\pi\_\{z\}e^\{\-\\Lambda\_\{z\}\(m\)\}\}\{1\-\\pi\_\{z\}\+\\pi\_\{z\}e^\{\-\\Lambda\_\{z\}\(m\)\}\}\.

###### Proof\.

The chain rule under𝒞i,s,z\(r−1\)\\mathcal\{C\}\_\{i,s,z\}^\{\(r\-1\)\}gives a likelihood ratio at moste−Λz​\(m\)e^\{\-\\Lambda\_\{z\}\(m\)\}, and Bayes’ rule gives Eq\. \([10](https://arxiv.org/html/2608.11235#S3.E10)\)\. Proposition[1](https://arxiv.org/html/2608.11235#Thmproposition1)makes endpoint disagreement a subset ofℬi,s\\mathcal\{B\}\_\{i,s\}\. ∎

Because CORA\-Diff accepts a residual candidate as soon as both gates first hold,\{sih=s,Zi,s=z\}=ℛi,s∩𝒢i,s∩ℱi,s\(m\)∩\{Zi,s=z\}=𝒞i,s,z\(m\)\\\{s\_\{i\}^\{h\}=s,Z\_\{i,s\}=z\\\}=\\mathcal\{R\}\_\{i,s\}\\cap\\mathcal\{G\}\_\{i,s\}\\cap\\mathcal\{F\}\_\{i,s\}^\{\(m\)\}\\cap\\\{Z\_\{i,s\}=z\\\}=\\mathcal\{C\}\_\{i,s,z\}^\{\(m\)\}\. Thus Eq\. \([10](https://arxiv.org/html/2608.11235#S3.E10)\) bounds disagreement under the conditional distribution of first\-hit states, not pointwise at a deterministic state\. If every stratum with positive first\-hit acceptance mass hasqz,r−\>0q\_\{z,r\}^\{\-\}\>0,πz≤π¯\\pi\_\{z\}\\leq\\bar\{\\pi\}, andλz,r≥λ¯\>0\\lambda\_\{z,r\}\\geq\\underline\{\\lambda\}\>0for allr≤mr\\leq m, averaging gives

R𝒟acc​\(δp,m\)≤π¯​e−m​λ¯1−π¯\+π¯​e−m​λ¯\.R\_\{\\mathcal\{D\}\}^\{\\mathrm\{acc\}\}\(\\delta\_\{p\},m\)\\leq\\frac\{\\bar\{\\pi\}e^\{\-m\\underline\{\\lambda\}\}\}\{1\-\\bar\{\\pi\}\+\\bar\{\\pi\}e^\{\-m\\underline\{\\lambda\}\}\}\.\(11\)Because the trajectory, analysis measure, and stratum\-specific constants depend onh=\(δp,m\)h=\(\\delta\_\{p\},m\), this is a configuration\-specific bound; threshold dependence is measured by the calibration sweep\. At\(0\.65,1\)\(0\.65,1\),g​\(δp\)≈0\.310g\(\\delta\_\{p\}\)\\approx 0\.310and onlyλz,1\\lambda\_\{z,1\}enters\. Supplementary Table S6 finds marginal prompt\-bootstrap upper bounds below one in five of six strata\. The selected operating point therefore exhibits the predicted contraction in every well\-supported stratum; only the sparsely populated highest\-confidence stratum remains statistically unresolved\.

Early acceptance can also change later predictions at unresolved positions\. In the fixed\-horizon analysis, letYQhY\_\{Q\}^\{h\}be the final CORA\-Diff output on the samenQn\_\{Q\}\-token generation canvas asYQ⋆Y\_\{Q\}^\{\\star\}\. We therefore define prompt\-level final\-output disagreement as

LQout​\(h\)=1nQ​∑i=1nQ𝕀​\[YQ,ih≠YQ,i⋆\],L\_\{Q\}^\{\\mathrm\{out\}\}\(h\)=\\frac\{1\}\{n\_\{Q\}\}\\sum\_\{i=1\}^\{n\_\{Q\}\}\\mathbb\{I\}\[Y\_\{Q,i\}^\{h\}\\neq Y\_\{Q,i\}^\{\\star\}\],\(12\)with population value

R𝒟out​\(h\)=𝔼Q∼𝒟​\[LQout​\(h\)\]\.R\_\{\\mathcal\{D\}\}^\{\\mathrm\{out\}\}\(h\)=\\mathbb\{E\}\_\{Q\\sim\\mathcal\{D\}\}\[L\_\{Q\}^\{\\mathrm\{out\}\}\(h\)\]\.\(13\)The accepted\-token quantity diagnoses local gate reliability, whereas the final\-output quantity captures downstream changes caused by early intervention\. Together they separate local acceptance fidelity from trajectory\-level effects; benchmark scores evaluate task correctness\.

Figure[1](https://arxiv.org/html/2608.11235#S1.F1)establishes the motivating association on unperturbed dense trajectories\. Supplementary Table S6 complements it with paired post\-intervention trajectories and directly tests Assumption[1](https://arxiv.org/html/2608.11235#Thmassumption1)on actual CORA\-Diff states\.

We next analyze the selector used in our experiments\. Let𝒞=\{Q1,…,QN\}\\mathcal\{C\}=\\\{Q\_\{1\},\\ldots,Q\_\{N\}\\\}be an independent calibration sample from𝒟\\mathcal\{D\}, letℋ\\mathcal\{H\}be a finite threshold grid fixed before calibration outcomes are examined, and leth0h\_\{0\}denote dense decoding\. For promptQQ, let𝒦Q\\mathcal\{K\}\_\{Q\}be its blocks and letSQ,bhS\_\{Q,b\}^\{h\}andSQ,bdenseS\_\{Q,b\}^\{\\mathrm\{dense\}\}be the executed and dense step counts for blockbb\. Define the prompt ratioρQ​\(h\):=∑bSQ,bh/∑bSQ,bdense∈\[0,1\]\\rho\_\{Q\}\(h\):=\\sum\_\{b\}S\_\{Q,b\}^\{h\}/\\sum\_\{b\}S\_\{Q,b\}^\{\\mathrm\{dense\}\}\\in\[0,1\]\. LetSQ​\(h\)∈\[0,1\]S\_\{Q\}\(h\)\\in\[0,1\]be its task score\. We write their population means asM𝒟​\(h\)M\_\{\\mathcal\{D\}\}\(h\)andρ𝒟​\(h\)\\rho\_\{\\mathcal\{D\}\}\(h\), and their calibration means asM^𝒞​\(h\)\\widehat\{M\}\_\{\\mathcal\{C\}\}\(h\)andρ^𝒞​\(h\)\\widehat\{\\rho\}\_\{\\mathcal\{C\}\}\(h\)\. We similarly define

R^𝒞r​\(h\)=1N​∑j=1NLQjr​\(h\),r∈\{acc,out\}\.\\widehat\{R\}\_\{\\mathcal\{C\}\}^\{r\}\(h\)=\\frac\{1\}\{N\}\\sum\_\{j=1\}^\{N\}L\_\{Q\_\{j\}\}^\{r\}\(h\),\\qquad r\\in\\\{\\mathrm\{acc\},\\mathrm\{out\}\\\}\.\(14\)For score toleranceτ\\tauand output\-disagreement toleranceϵ\\epsilon, the reported empirical rule has the form

h^\\displaystyle\\widehat\{h\}∈argminh∈ℋρ^𝒞​\(h\),\\displaystyle\\in\\operatorname\*\{argmin\}\_\{h\\in\\mathcal\{H\}\}\\widehat\{\\rho\}\_\{\\mathcal\{C\}\}\(h\),\(15\)s\.t\.M^𝒞​\(h\)\\displaystyle\\text\{s\.t\.\}\\quad\\widehat\{M\}\_\{\\mathcal\{C\}\}\(h\)≥M^𝒞​\(h0\)−τ,R^𝒞out​\(h\)≤ϵ\.\\displaystyle\\geq\\widehat\{M\}\_\{\\mathcal\{C\}\}\(h\_\{0\}\)\-\\tau,\\quad\\widehat\{R\}\_\{\\mathcal\{C\}\}^\{\\mathrm\{out\}\}\(h\)\\leq\\epsilon\.
###### Proposition 3\(Uniform bound for the reported selector\)\.

Letℋ0=ℋ∪\{h0\}\\mathcal\{H\}\_\{0\}=\\mathcal\{H\}\\cup\\\{h\_\{0\}\\\}andβN=log⁡\(8​\|ℋ0\|/α\)/\(2​N\)\.\\beta\_\{N\}=\\sqrt\{\\log\(8\|\\mathcal\{H\}\_\{0\}\|/\\alpha\)/\(2N\)\}\.With probability at least1−α1\-\\alpha, the sample means of task score, prompt step ratio, accepted\-token disagreement, and output disagreement are all withinβN\\beta\_\{N\}of their population means, simultaneously overh∈ℋ0h\\in\\mathcal\{H\}\_\{0\}\. Consequently, the feasible choice in Eq\. \([15](https://arxiv.org/html/2608.11235#S3.E15)\) obeys

M𝒟​\(h^\)≥M𝒟​\(h0\)−τ−2​βN,R𝒟out​\(h^\)≤ϵ\+βN\.M\_\{\\mathcal\{D\}\}\(\\widehat\{h\}\)\\geq M\_\{\\mathcal\{D\}\}\(h\_\{0\}\)\-\\tau\-2\\beta\_\{N\},\\qquad R\_\{\\mathcal\{D\}\}^\{\\mathrm\{out\}\}\(\\widehat\{h\}\)\\leq\\epsilon\+\\beta\_\{N\}\.\(16\)

The supplement proves the proposition using Hoeffding’s inequality\(Hoeffding[1963](https://arxiv.org/html/2608.11235#bib.bib70)\)and a union bound\. For i\.i\.d\. calibration and deployment prompts, it quantifies the population slack induced by data\-dependent selection\. Benchmark scores assess correctness, while cross\-task transfer is evaluated empirically\. Within each fixed\-canvas task and budget, every prompt has the same dense denominator in this ratio\. The prompt mean therefore equals the aggregate pass\-count ratio reported in our fixed\-horizon tables\.

#### From acceptance to runtime\.

When the original rule and CORA\-Diff jointly resolve the active block, the decoder skips its remaining dense passes\. We reportρstep\\rho\_\{\\mathrm\{step\}\}, the executed\-step count divided by the fixed dense horizon; every executed step remains dense\. The supplement gives the derivation, complete algorithm, state, and dense\-recovery case\.

## 4Experiments

Table 1:Main results under the matched Learn2PD\-style LLaDA protocol\. Metrics are Flex EM, MATH accuracy, and code pass@1\. CORA\-Diff uses the calibration\-selected configuration\(δp,m\)=\(0\.65,1\)\(\\delta\_\{p\},m\)=\(0\.65,1\)\. Original denotes the unmodified fixed\-horizon dense decoder\. Time is the total wall\-clock time over the complete test split; Time and Tok/s are three\-run means\. Spd\. and Ratio denote speedup and denoising\-step ratio\. Cache reuse is disabled\. Dashes mark unavailable step counts\. Raw runs and confidence intervals are in the supplement\.Table 2:EOS\-aware deployment at maximum length and budget 1024\. Paired cells report mean active length/executed blocks \(Len\./Blk\.\), mean/P90 latency in seconds \(Lat\.\), and speedup over fixed\-horizon Original/Original\+\+EoTP \(Spd\.\)\.### 4\.1Experimental Setup

The main comparison follows the Learn2PD\-style LLaDA\-8B\-Instruct protocol on four benchmarks\(Nieet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib20); Baoet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib24); Cobbeet al\.[2021](https://arxiv.org/html/2608.11235#bib.bib56); Hendryckset al\.[2021](https://arxiv.org/html/2608.11235#bib.bib57); Chenet al\.[2021](https://arxiv.org/html/2608.11235#bib.bib59); Austinet al\.[2021b](https://arxiv.org/html/2608.11235#bib.bib60)\)\. We reproduce all baselines from official implementations under shared evaluation factors\(Liet al\.[2026a](https://arxiv.org/html/2608.11235#bib.bib39); Kimet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib26),[2026](https://arxiv.org/html/2608.11235#bib.bib68)\)\. All runs use complete test splits, batch size 1, bfloat16, temperature 0, and one RTX 5090; the supplement gives seeds and prompts\.

#### Calibration and configuration selection\.

We select\(δp,m\)\(\\delta\_\{p\},m\)on 1,000 GSM8K training prompts disjoint from all reported evaluation sets, using the same 3\-shot construction, harness, decoding configuration, and scoring as the GSM8K test evaluation\. The prespecified rule requires Flex EM within 0\.5 percentage points of dense and final\-output disagreement at most 1\.0%, then minimizes step ratio\. Dense Flex EM is 0\.780 \(floor 0\.775\);\(0\.65,1\)\(0\.65,1\)is selected with 0\.779 Flex EM, 0\.79% disagreement, and ratio 0\.2020\. Only this held\-out subset affects selection; no reported test metric or runtime is used for tuning\. The pair remains fixed in all subsequent experiments\. Proposition[3](https://arxiv.org/html/2608.11235#Thmproposition3)characterizes selection under the same\-distribution assumption; task and backbone transfer are empirical\. Supplementary Table S1 gives the complete sweep\.

#### Baseline reproduction and controls\.

Each method keeps its released internal rule and recommended thresholds\. Supplementary Table S2 gives exact settings, official\-reference configurations, and the CreditDecoding exclusion\. Cache reuse and sparse execution are disabled in the main comparison\. CORA\-Diff is selected by our calibration rule, whereas reproduced baselines retain released thresholds or checkpoints\. The comparison therefore provides a controlled evaluation of released operating points under matched execution factors\.

### 4\.2Matched\-Protocol Results

Table[1](https://arxiv.org/html/2608.11235#S4.T1)compares the standard 256/256 setting with the longer 1024/1024 setting\.

#### Overall quality–efficiency trade\-off\.

CORA\-Diff has the lowest measured runtime in all eight task–length settings\. Under the fixed\-horizon mechanism\-isolation protocol, it reaches4\.34×4\.34\\times–9\.49×9\.49\\timesspeedup at 256/256 and10\.68×10\.68\\times–13\.14×13\.14\\timesat 1024/1024\. Against Learn2PD, the closest runtime baseline, its measured mean speedup is 9\.1%–30\.9% higher\.

#### Effect of the denoising horizon\.

CORA\-Diff executes 10\.10%–22\.78% of dense steps at 256/256 and 7\.56%–8\.94% at 1024/1024\. The lower 1024/1024 ratios are consistent with a larger late region of stable or redundant denoising work\. Measured speedup reaches 92\.7%–99\.5% of the ideal1/ρstep1/\\rho\_\{\\mathrm\{step\}\}limit\. The remaining gap is consistent with bookkeeping, synchronization, and data\-movement overhead\.

#### Task\-dependent stopping behavior\.

At 256/256, the step ratio varies from 0\.1010 on MATH to 0\.2278 on HumanEval, whereas all four 1024/1024 ratios lie in the narrow 0\.0756–0\.0894 range\. A long horizon therefore creates shared late\-stage redundancy that dominates task differences\. At 256/256, speed depends more on when each block’s last unresolved positions stabilize, rather than on task difficulty alone\.

#### Comparison with baselines\.

CORA\-Diff uses fewer reported steps than Prophet, KLASS, and DAPD\. DAPD preserves strong 256/256 scores but accepts conservatively; Prophet uses answer\-level convergence, KLASS tests distributional stability, and DAPD models token dependencies\. At their reported operating points, these criteria retain more denoising work\. Learn2PD is the closest speed baseline and sometimes scores higher, but uses a trained filter\. CORA\-Diff’s measured speedup is 9\.1%–30\.9% higher than Learn2PD’s, and it is the lowest\-latency method in all eight matched settings without a trained acceptance filter\.

#### Executed steps explain the speed gap\.

For methods reporting step counts, ratio closely tracks wall\-clock speed\. On GSM8K 1024/1024, CORA\-Diff uses a 0\.0756 ratio and reaches13\.14×13\.14\\times, versus ratios 0\.1590–0\.558 and speedups1\.79×1\.79\\times–5\.92×5\.92\\timesfor Prophet, KLASS, and DAPD\. The values are not exact reciprocals because controller and data\-movement costs differ, but they locate the main gain in earlier block completion\. CORA\-Diff tests only residual positions with same\-pass signals, converting local acceptance into skipped dense passes\.

#### Score changes and disagreement\.

Across the eight settings, CORA\-Diff’s observed metric change from Original ranges from−1\.22\-1\.22to\+1\.14\+1\.14points, and five scores match or exceed dense decoding\. Selection jointly constrains score and output disagreement, allowing aggressive step reduction while preserving task quality\. Endpoint agreement measures decoder fidelity, while benchmark accuracy measures task utility; using both prevents speed from being optimized at the expense of answer\-critical tokens\.

#### Scope of the fixed\-horizon comparison\.

The table controls shared factors; official settings are in the supplement\. The fixed 1024\-token canvas is a mechanism\-isolation stress test of repeated denoising\. We next remove post\-response work with a shared EOS\-aware controller to measure deployment benefit\.

### 4\.3Deployment and Robustness Analysis

#### EOS\-aware deployment\.

At maximum length and budget 1024, only a committed EOS removes the suffix and future blocks\. This removes post\-response work, while CORA\-Diff reduces denoising before EOS\. Table[2](https://arxiv.org/html/2608.11235#S4.T2)shows2\.70×2\.70\\timesand3\.32×3\.32\\timesspeedups over EOS\-aware dense decoding\. Mean and P90 latency beat Learn2PD, although HumanEval scores lower; similar lengths make shorter outputs an unlikely main cause\. The result is therefore consistent with CORA\-Diff removing substantial pre\-EOS denoising rather than relying mainly on earlier truncation\.

#### Cross\-backbone transfer and cache compatibility\.

Supplementary Table S3 reports3\.18×3\.18\\times–3\.53×3\.53\\timeson Dream without retuning and cache combinations up to53\.65×53\.65\\times\(Yeet al\.[2025](https://arxiv.org/html/2608.11235#bib.bib22); Baoet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib24); Wuet al\.[2026](https://arxiv.org/html/2608.11235#bib.bib35)\)\. These results demonstrate transfer to a second backbone and composability with cache reuse\.

#### Component ablation\.

Table[3](https://arxiv.org/html/2608.11235#S4.T3)reports independent complete\-test\-set runs, separate from Table S1 and unused for selection\. At frozenδp=0\.65\\delta\_\{p\}=0\.65, one persistence check improves confidence\-only Flex EM from 0\.7301 to 0\.7794, while Tok/s falls from 43\.51 to 39\.12 \(10\.1%\) and ratio rises from 0\.1783 to 0\.2012\. Persistence alone gives 0\.7557 Flex EM at 35\.06 Tok/s\. Two checks reach ratio 0\.2361 and 34\.47 Tok/s without improving overm=1m=1, supporting the combined one\-check rule\.

Table 3:Independent post\-selection component ablation on the complete GSM8K test split \(256/256256/256,δp=0\.65\\delta\_\{p\}=0\.65\); not used for selection\. Tok/s averages three runs; Flex EM and Ratio are deterministic at temperature 0\.

## 5Conclusion, Limitations, and Future Work

CORA\-Diff retains the original transfer rule and terminates resolved blocks without a learned acceptance model\. It is fastest in all eight matched settings, gives2\.70×2\.70\\times–3\.32×3\.32\\timesEOS\-aware speedups, and reaches13\.14×13\.14\\timesin fixed\-horizon mechanism isolation\. Theory and paired trajectories connect confidence and persistence to endpoint agreement, explaining the observed reduction in dense computation\.

#### Limitations and future work\.

Paired validation supports five of six strata; one sparse stratum remains data\-limited, and broader deployment tests are future work\.

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