Spec-AUF: Accept-Until-Fail Training under Train-Inference Misalignment for Masked Block Drafters

# Spec-AUF: Accept-Until-Fail Training under Train-Inference Misalignment for Masked Block Drafters
Source: [https://arxiv.org/html/2607.01893](https://arxiv.org/html/2607.01893)
###### Abstract

Speculative decoding accelerates autoregressive generation by drafting a block of tokens that the target model verifies left\-to\-right, committing only the longest accepted prefix\. Block \(DLM\-style\) drafters predict the whole block in parallel, which is fast but trained with a full\-block cross\-entropy that supervises every position against the gold continuation—even though inference discards every token after the first rejection\. Recent acceptance\-aware objectives patch this by reweighting the full\-block loss; we instead use teacher\-forced learning as a motivation for how supervision should concentrate on the accepted prefix\. A mask\-only block drafter has no input\-side channel for gold\-prefix conditioning, so AUF approximates that prefix\-sensitive supervision on the loss side by keeping the cross\-entropy support only through the drafter’s first predicted failure\. AUF is a single, detached change to the CE support—no auxiliary objective, no verifier rollouts, and no change to the inference pipeline or the exactness contract\. Within fixed drafter backbones and serving settings on Qwen3\-8B, AUF raises the DFlash drafter’s average emitted lengthτ\\tau, averaged over six benchmarks, from2\.402\.40to2\.612\.61, with a gain on every benchmark, and transfers to Domino’s two\-branch head \(2\.562\.56to2\.682\.68\)\. Two findings sharpen the picture: the decay\-only baseline reaches*higher*token accuracy on the shared block mask yet decodes*worse*, and on DFlash, once AUF truncates the support, the standard exponential position\-decay weighting becomes empirically inert\.

## 1Introduction

Speculative decoding \(SD\) accelerates autoregressive language\-model inference by letting a lightweight draft model propose several future tokens and letting the target model verify them in one parallel pass\(Leviathanet al\.[2023](https://arxiv.org/html/2607.01893#bib.bib1); Chenet al\.[2023](https://arxiv.org/html/2607.01893#bib.bib2)\)\. Because verification accepts only the longest target\-consistent prefix, the practical speedup of SD is governed less by isolated token accuracy than by the draft model’s ability to produce a consecutive prefix that the target will accept\. A drafter that predicts later tokens correctly after an early mistake still wastes those predictions: the verifier rejects the suffix once the prefix is broken\.

This observation changes how draft\-model training should be viewed\. Standard alignment objectives train the drafter to match target tokens over a full block, often with a hand\-designed position prior — a fixed weight that decays with block position, encoding the inductive bias that earlier tokens matter more \(DFlash, for instance, uses an exponential decay\(Chenet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib7)\)\)\. These objectives recognize that early positions matter more, but they still supervise tokens whose contribution to throughput is conditional on all previous draft tokens being accepted\. Draft\-model training is therefore not only a token\-alignment problem; it must also reflect the left\-to\-right prefix contract used by the verifier\.

Our starting point is the analogy to autoregressive draft\-model training\. With teacher\-forced maximum likelihood, an autoregressive drafter receives the gold prefix on its input side, so the loss at positioniiis conditioned on the event that positions<i<iare already correct\(Liet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib5)\)\. Gold supervision is the strong signal, and the design question is which positions are entitled to receive it\. A masked or diffusion\-style block drafter such as DFlash cannot obtain this conditioning from its input at all: the block positions are predicted in parallel from masked tokens\. We therefore approximate that prefix\-sensitive supervision on the loss side\. Accept\-Until\-Fail \(AUF\) keeps the gold\-target cross\-entropy only through the first draft error: the accepted prefix and the first failing token remain active, while all later positions are masked out\.

The closest related line begins with GRIFFIN, which also drops the draft loss once an earlier target token falls outside the model’s Top\-KKpredictions\(Huet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib3)\); AUF shares this “stop supervising once the prefix is broken” intuition but differs in both criterion and mechanism, while the soft\-weighting line \(decay, D\-PACE\) keeps a full\-block support and re\-approximates the conditioning with position weights instead\(Wuet al\.[2026a](https://arxiv.org/html/2607.01893#bib.bib8)\)\. Section[3](https://arxiv.org/html/2607.01893#S3)places these treatments of the same training–verification mismatch on one axis; what we add is a teacher\-forcing\-motivated reading and the mask\-only setting it applies to, where the prefix conditioning has no input\-side channel and must act on the loss side\.

This direction is not an obvious win\. D\-PACE reports that a GRIFFIN\-style Top\-3 prefix\-mask baseline*underperforms*even the decayed\-CE DFlash baseline on Qwen3\-4B\(Wuet al\.[2026a](https://arxiv.org/html/2607.01893#bib.bib8)\)— but Top\-3*membership*is GRIFFIN’s AR\-tuned choice, not the same operator as truncation at the first*greedy*\(argmax\) error \(Section[3](https://arxiv.org/html/2607.01893#S3)\)\. On Qwen3\-8B our exact\-match truncation improvesτ\\tauover the decayed\-CE baseline on DFlash across all six evaluated benchmarks, and transfers to Domino’s two\-branch head across the same benchmarks\. That a coarse Top\-3 mask helps in an AR drafter yet hurts on a block drafter, while exact first\-error truncation helps, is itself evidence that prefix\-aware supervision does not transfer trivially from AR to mask\-only drafters — the gap this paper is about\.

On DFlash, AUF fully replaces this hand\-designed position prior: once the support is truncated at the first predicted error, applying the exponential decay*inside*that support leavesτ\\tauunchanged on all six benchmarks \(Section[5\.1](https://arxiv.org/html/2607.01893#S5.SS1)\)\. The position\-decay weighting is thus redundant under AUF rather than complementary to it\. This is not only a simplification of the loss: AUF removes a fixed, manually tuned inductive\-bias term and lets the model’s own first\-failure position decide where supervision lands — replacing a hand\-set position prior, and its decay\-rate hyperparameterγd\\gamma\_\{d\}, with a model\-decided support\. Whether this model\-decided support remains the better default beyond the fixed settings studied here is a question we return to in Section[6](https://arxiv.org/html/2607.01893#S6)\.

## 2Preliminaries

#### Speculative decoding\.

Letpθp\_\{\\theta\}be the target model andqψq\_\{\\psi\}be a draft model\. At each SD iteration, the draft model proposes a block ofBBcandidate tokens\(y^1,…,y^B\)\(\\hat\{y\}\_\{1\},\\ldots,\\hat\{y\}\_\{B\}\)\. The target model verifies these candidates left\-to\-right in one parallel forward pass and accepts the longest prefix that matches the target decoding policy\. Let

A=max⁡\{k:y^i=yi​∀i≤k\}A=\\max\\\{k:\\hat\{y\}\_\{i\}=y\_\{i\}\\;\\;\\forall i\\leq k\\\}denote the number of accepted draft tokens before the verifier emits the next target token\. In our SGLang serving path the reported acceptance length isτ=A\+1\\tau=A\+1, where the extra token is this verifier\-emitted correction token\. For a fixed implementation and hardware setting, higher expectedτ\\taudirectly reduces the number of target verification rounds per generated token, so draft accuracy matters primarily through its effect on consecutive prefix acceptance\.

#### Parallel DLM/block drafters\.

DFlash is a representative block drafter: it predicts a full block in one draft forward pass using target hidden\-state features and masked block tokens\(Chenet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib7)\)\. This removes the sequential drafting dependency inside the block, but it creates a mismatch with SD verification\. The DLM\-style drafter predicts positions in parallel, while the target verifier consumes them strictly left\-to\-right\. A correct prediction at positionjjis useful only if all previous positions are also accepted\.

#### Train–inference mismatch in block objectives\.

The same mismatch can be phrased as an objective gap\. DFlash\-style training uses block\-level masked CE, optionally with a hand\-designed position decay, while inference measures an accepted streak under a left\-to\-right verifier\. Thus, training can reward later\-token reconstruction even when those later tokens would be discarded after an earlier rejection\. SpecDiff\-2 makes an analogous point for diffusion drafters: diffusion models learn joint denoising distributions over blocks, whereas autoregressive verifiers make local prefix\-conditional token decisions\(Sandleret al\.[2025](https://arxiv.org/html/2607.01893#bib.bib9)\)\. It addresses this gap by optimizing a streak\-distillation objective over verifier\-sampled teacher trajectories and by adding test\-time self\-selection\. AUF follows the same high\-level diagnosis but uses a cheaper hard\-label approximation: it keeps the existing DFlash/Domino drafter and changes only which CE terms are active\.

Concretely, letℓi​\(ψ\)=−log⁡qψ,i​\(yi∣s,\[MASK\]1:B\)\\ell\_\{i\}\(\\psi\)=\-\\log q\_\{\\psi,i\}\(y\_\{i\}\\mid s,\[\\mathrm\{MASK\}\]^\{1:B\}\)be the masked\-block CE at positionii, where all future positions are predicted in parallel\. The DFlash objective is a weighted additive reconstruction loss,

ℒDFlash=∑i=1Bmi​wi​ℓi​\(ψ\)∑i=1Bmi​wi,wi=exp⁡\(−\(i−1\)/γd\),\\mathcal\{L\}\_\{\\mathrm\{DFlash\}\}=\\frac\{\\sum\_\{i=1\}^\{B\}m\_\{i\}w\_\{i\}\\ell\_\{i\}\(\\psi\)\}\{\\sum\_\{i=1\}^\{B\}m\_\{i\}w\_\{i\}\},\\qquad w\_\{i\}=\\exp\(\-\(i\-1\)/\\gamma\_\{d\}\),wheremim\_\{i\}is the validity mask andwiw\_\{i\}is the fixed decay\. This loss can emphasize early positions, but every valid suffix token remains an independent training target\. The speculative verifier instead advances by an accepted streak,

𝔼​\[τ∣s\]=1\+𝔼y^1:B∼qψ​\[∑k=1B∏i=1kαi​\(s,y^<i,y^i\)\],\\mathbb\{E\}\[\\tau\\mid s\]=1\+\\mathbb\{E\}\_\{\\hat\{y\}\_\{1:B\}\\sim q\_\{\\psi\}\}\\left\[\\sum\_\{k=1\}^\{B\}\\prod\_\{i=1\}^\{k\}\\alpha\_\{i\}\(s,\\hat\{y\}\_\{<i\},\\hat\{y\}\_\{i\}\)\\right\],whereαi\\alpha\_\{i\}is the conditional acceptance probability at positioniigiven that the previousi−1i\-1draft tokens survived\. The objective gap is therefore structural: the decayed CE optimizes an additive per\-position surrogate, while inference rewards a product\-gated prefix event\.

#### A unified weighted\-CE view\.

Up to per\-batch normalization, the decayed CE, D\-PACE’s dynamic weights, and the GRIFFIN\-style prefix mask are all instances of a single weighted cross\-entropy,

ℒ​\(ψ\)=∑i=1Bmi​ci​ℓi​\(ψ\)∑i=1Bmi​ci,\\mathcal\{L\}\(\\psi\)=\\frac\{\\sum\_\{i=1\}^\{B\}m\_\{i\}\\,c\_\{i\}\\,\\ell\_\{i\}\(\\psi\)\}\{\\sum\_\{i=1\}^\{B\}m\_\{i\}\\,c\_\{i\}\},\(1\)differing only in the*per\-position credit*cic\_\{i\}assigned to each CE term; in all of themcic\_\{i\}is detached from the gradient, performing credit assignment without itself being optimized\. Up to the constant correction\-token offset inτ=A\+1\\tau=A\+1, the natural smooth surrogate for accepted length is the cumulative\-confidence proxy used by D\-PACE\(Wuet al\.[2026a](https://arxiv.org/html/2607.01893#bib.bib8)\),S~=∑k=1B∏i≤kqψ,i​\(yi\)\\tilde\{S\}=\\sum\_\{k=1\}^\{B\}\\prod\_\{i\\leq k\}q\_\{\\psi,i\}\(y\_\{i\}\), whose gradient decomposes into a weighted sum of per\-position score gradients,

∇ψS~=∑i=1Bgi​∇ψlog⁡qψ,i​\(yi\),gi=\(∏l≤iqψ,l​\(yl\)\)​fi,\\nabla\_\{\\psi\}\\tilde\{S\}=\\sum\_\{i=1\}^\{B\}g\_\{i\}\\,\\nabla\_\{\\psi\}\\log q\_\{\\psi,i\}\(y\_\{i\}\),\\quad g\_\{i\}=\\Big\(\\textstyle\\prod\_\{l\\leq i\}q\_\{\\psi,l\}\(y\_\{l\}\)\\Big\)\\,f\_\{i\},\(2\)with continuation valuefi=1\+∑m\>i∏l=i\+1mqψ,l​\(yl\)f\_\{i\}=1\+\\sum\_\{m\>i\}\\prod\_\{l=i\+1\}^\{m\}q\_\{\\psi,l\}\(y\_\{l\}\)\. The creditgig\_\{i\}factorizes into a*prefix\-acceptance gate*∏l≤iqψ,l​\(yl\)\\prod\_\{l\\leq i\}q\_\{\\psi,l\}\(y\_\{l\}\)— a smooth estimate of the probability that the draft prefix through positioniiis accepted — times a continuation value\. The gate is the dominant factor: D\-PACE reports that the cumulative\-only weight recovers most of the gain over fixed decay while the continuation\-only variant is far weaker\(Wuet al\.[2026a](https://arxiv.org/html/2607.01893#bib.bib8)\)\. The reference signal is therefore that a position’s training credit should scale with the probability that its prefix is accepted, and any objective whose credit ignores this gate is structurally misaligned with the inference reward\. SpecDiff\-2 closes the gap most directly by optimizing a soft prefix\-product reward along verifier\-sampled teacher continuations, at the cost of those rollouts and a distillation procedure\(Sandleret al\.[2025](https://arxiv.org/html/2607.01893#bib.bib9)\); the present work instead approximates the same gate with a hard, single\-sample plug\-in, developed in Section[4](https://arxiv.org/html/2607.01893#S4)\.

![Refer to caption](https://arxiv.org/html/2607.01893v1/x1.png)Figure 1:Teacher\-forced training for an autoregressive draft model\. The model receives the gold prefix as input and predicts shifted target tokens, so each CE term is trained under the prefix\-correct condition\.
#### Teacher forcing as the source of the design\.

The reason this is natural is teacher forcing\. In autoregressive training the model predictsyiy\_\{i\}conditioned on the gold prefixy<iy\_\{<i\}, making the loss at positioniia conditional\-prefix loss by construction \(Figure[1](https://arxiv.org/html/2607.01893#S2.F1)\)\. The opposite choice — training on self\-generated prefixes while still mapping them to gold next tokens — creates a distribution mismatch: once the prefix is corrupted, the supervised input–output pair may not correspond to the data distribution\(Huszár[2015](https://arxiv.org/html/2607.01893#bib.bib4)\)\. The practical reading is that gold supervision is the strong signal: EAGLE\-3 keeps gold shifted tokens for exactly this reason, and generates subsequent hidden states from its own training\-time rollout only because those intermediate features have no gold counterpart to teacher\-force against, not because self\-generated inputs are preferable\(Liet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib5)\)\. The open question for a block drafter is therefore not whether to use gold targets — they are the strong signal — but which positions can legitimately receive gold supervision\. This question is sharp in speculative decoding: Domino can answer it on the*input*side, because its causal branch consumes ground\-truth prefix tokens\(Huanget al\.[2026](https://arxiv.org/html/2607.01893#bib.bib6)\), whereas a masked block drafter has no such channel and must answer it on the loss side — the route AUF takes, developed in Section[4](https://arxiv.org/html/2607.01893#S4)\.

## 3Related Work

#### Acceptance\-aware block\-drafter objectives\.

The training objective we modify is shared, up to per\-position weighting, across a growing family of methods\. GRIFFIN introduces a prefix mask that removes the loss at positionjjif an earlier target token is outside the draft model’s Top\-KKpredictions, propagating the mask through a short window\(Huet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib3)\)\. D\-PACE instead keeps the CE support intact but replaces fixed position decay with dynamic weights derived from an accepted\-length surrogate\(Wuet al\.[2026a](https://arxiv.org/html/2607.01893#bib.bib8)\), and the left\-to\-right focal objective for diffusion drafters adds a first\-error focal term on top of a retained position decay\(Whalenet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib10)\)\. These three are different treatments of the same training–verification mismatch\. AUF takes the hardest, most direct form of the signal: the drafter first emits a greedy block, the first exact \(*argmax*\) token mismatch defines the SD prefix boundaryj∗j^\{\*\}, and CE is applied only up to that boundary\. The criterion and the mechanism both differ from GRIFFIN — an*argmax*mismatch on the model’s own greedy block, not Top\-KKmembership, and a clean truncation of all later positions, not a windowed product that can re\-activate — and from D\-PACE’s soft reweighting and the focal term’s additive penalty\. AUF is not GRIFFIN’sK=1K\{=\}1special case: GRIFFIN never defines a first\-error boundary or truncates past it\.

Table[1](https://arxiv.org/html/2607.01893#S3.T1)makes the relationship precise: all of these objectives are the*same*weighted block CE, differing only in the per\-position creditcic\_\{i\}, and only AUF setscic\_\{i\}from an exact prefix\-acceptance test on the model’s own greedy block — the hard limit of the soft prefix\-acceptance gate that the other methods grade \(Section[2](https://arxiv.org/html/2607.01893#S2)\), augmented with the breaker token\.

Table 1:Block\-drafter CE objectives as instances of one weighted block CEℒ∝∑imi​ci​ℓi​\(ψ\)\\mathcal\{L\}\\propto\\sum\_\{i\}m\_\{i\}\\,c\_\{i\}\\,\\ell\_\{i\}\(\\psi\), differing only in the per\-position creditcic\_\{i\}\(gate defined in Section[2](https://arxiv.org/html/2607.01893#S2)\)\. “Graded credit” marks soft gates and “verifier rollout” marks methods that sample teacher trajectories frompθp\_\{\\theta\}\. Only AUF truncates the active support to the accepted prefix plus the breaker\{1,…,j∗\}\\\{1,\\ldots,j^\{\*\}\\\}; every prior objective keeps the full\-block support and only reweights it\.
#### The soft\-reweighting and divergence\-shaping lines\.

Beyond our nearest neighbors, a broader set of recent methods keeps a full\-block support and changes how it is weighted or scored\. PARD\-2 reweights each position by a cumulative product of target confidences, again replacing the fixed decay\(Anet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib16)\); LK Losses optimize a direct acceptance\-rate surrogate\(Samarinet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib17)\)and Halfway couples drafter and target in a joint acceptance objective\(Nistor[2026](https://arxiv.org/html/2607.01893#bib.bib21)\), but both retain an exponential position decay; and VSD lifts the objective from token likelihood to sequence\-level acceptance\(Zouet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib19)\)\. The common thread is a full\-block soft support, or a decay term left in place\. AUF differs in one structural respect: it lets the drafter’s own first greedy error*define*the support and then removes the decay, rather than reweighting, augmenting, or re\-shaping a support that still spans the block\.

#### Block\- and diffusion\-style drafters\.

The drafters we build on predict a block in parallel\. DFlash is the block\-diffusion baseline whose masked\-block CE with exponential decay we target\(Chenet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib7)\), and Domino adds a causal branch that consumes ground\-truth prefix tokens, giving it the input\-side conditioning a mask\-only drafter lacks\(Huanget al\.[2026](https://arxiv.org/html/2607.01893#bib.bib6)\); these are the two backbones we evaluate\. Masked\-diffusion LMs can be trained as weighted masked\-CE objectives\(Sahooet al\.[2024](https://arxiv.org/html/2607.01893#bib.bib11)\), and block diffusion interpolates between autoregressive and full diffusion via the block size\(Arriolaet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib12)\): larger blocks expose more parallelism but rely more on intra\-block bidirectional aggregation\. Curricula that grow the block from next\-token to next\-block prediction ease adaptation from AR checkpoints and stabilize large\-block generation\(Tianet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib13); Wuet al\.[2026b](https://arxiv.org/html/2607.01893#bib.bib14)\), and TraceRL argues that DLM post\-training should use information from the inference trajectory rather than an off\-policy surrogate alone\(Wanget al\.[2025](https://arxiv.org/html/2607.01893#bib.bib15)\)\. Together these motivate treating AUF’s active support as a training\-dynamics object, not only a static loss mask\. Other recent parallel drafters scale a different axis — D2SD pairs two diffusion drafters\(Zhanget al\.[2026a](https://arxiv.org/html/2607.01893#bib.bib18)\), JetSpec widens parallel tree drafting\(Huet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib20)\), and HCSpec cascades two tiers\(Zhanget al\.[2026b](https://arxiv.org/html/2607.01893#bib.bib22)\)— and are orthogonal to the training\-objective change AUF makes, which leaves the architecture and inference pipeline untouched\.

#### Teacher forcing in autoregressive drafters\.

The prefix\-sensitive supervision that motivates AUF is native to autoregressive drafters, which receive the gold prefix on their input\(Liet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib5)\); GRIFFIN’s loss mask supplements this input\-side channel rather than substituting for it\. A mask\-only block drafter has no such channel, so the same intuition has to act on the loss side \(Section[4](https://arxiv.org/html/2607.01893#S4)\)\. This setting difference, not the masking operator, is what we claim is new\.

## 4Method

![Refer to caption](https://arxiv.org/html/2607.01893v1/x2.png)Figure 2:Full\-block decayed CE versus AUF for a masked block drafter\. Left: the block is predicted in parallel, and the full\-block decayed CE assigns nonzero credit to suffix tokens after the first greedy error\. Right: AUF computes the first mismatchj∗j^\{\*\}from detached greedy predictions and keeps CE active only on positions1:j∗1\{:\}j^\{\*\}, the accepted prefix plus the first failing token\.#### Why fixed decay is train–inference inconsistent\.

The unified view of Section[2](https://arxiv.org/html/2607.01893#S2)makes the design target explicit: a position’s creditcic\_\{i\}in equation[1](https://arxiv.org/html/2607.01893#S2.E1)should track the prefix\-acceptance gate∏l≤iqψ,l​\(yl\)\\prod\_\{l\\leq i\}q\_\{\\psi,l\}\(y\_\{l\}\)of equation[2](https://arxiv.org/html/2607.01893#S2.E2)\. The hand\-designed position prior setsci=wi=exp⁡\(−\(i−1\)/γd\)c\_\{i\}=w\_\{i\}=\\exp\(\-\(i\-1\)/\\gamma\_\{d\}\), a function of position alone, and is inconsistent with that gate in two ways\. First,*credit on unrealizable positions*: when the prefix has already broken at some positionj<ij<i, the gate is near zero butwiw\_\{i\}remains strictly positive, so the decayed CE spends gradient raisingqψ,i​\(yi\)q\_\{\\psi,i\}\(y\_\{i\}\)on positions the verifier has already abandoned — the block\-drafter form of exposure bias\. Second,*a static bottleneck*: the gate is data\- and model\-dependent and moves rightward as the drafter improves, whereaswiw\_\{i\}is fixed before training, so a schedule set ex ante cannot track the position that currently limits acceptance\. Fixed decay does encode the correct prior that earlier positions matter more — which is why it beats uniform CE — but it is a position prior, not a prefix\-acceptance signal, and the two diverge exactly on the examples that determineAA\.

#### AUF as the hard plug\-in of the gate\.

AUF replaces the fixed weight with the maximum\-a\-posteriori, single\-sample plug\-in of the same gate\. Replacing each soft factorqψ,l​\(yl\)q\_\{\\psi,l\}\(y\_\{l\}\)in the prefix product by its greedy realization𝟏​\[y^l=yl\]\\mathbf\{1\}\[\\hat\{y\}\_\{l\}=y\_\{l\}\]collapses the gate to the indicator∏l≤i𝟏​\[y^l=yl\]=𝟏​\[i<j∗\]\\prod\_\{l\\leq i\}\\mathbf\{1\}\[\\hat\{y\}\_\{l\}=y\_\{l\}\]=\\mathbf\{1\}\[i<j^\{\*\}\], wherej∗j^\{\*\}is the first greedy mismatch\. This hard gate activates only the accepted prefix\{1,…,j∗−1\}\\\{1,\\ldots,j^\{\*\}\{\-\}1\\\}; AUF extends the support by one position to include the failing tokenj∗j^\{\*\}itself, because it is the decision that breaks the accepted prefix and the position whose improvement directly extendsAA\. The resulting support\{1,…,j∗\}\\\{1,\\ldots,j^\{\*\}\\\}is therefore not the gate alone but the gate plus the breaker — the minimal superset that covers every position relevant to the next unit of acceptance\. AUF is thus a zero\-temperature, hard version of the prefix\-acceptance gate that D\-PACE estimates softly, augmented with the single token whose CE gradient most directly pushesj∗j^\{\*\}rightward, applied as a0/10/1support instead of a graded weight\. Unlike fixed decay it retargets automatically: as the drafter improves,j∗j^\{\*\}moves right and the active support expands with no schedule\. We give the loss next, then return to what this hard plug\-in gives up\.

#### Accept\-Until\-Fail CE\.

For a training block of lengthBB, letV=\{i:mi=1\}V=\\\{i:m\_\{i\}=1\\\}be the set of natively valid positions \(the validity mask of equation[1](https://arxiv.org/html/2607.01893#S2.E1)\), letyiy\_\{i\}be the target token andy^i=arg⁡max⁡qψ​\(⋅\)i\\hat\{y\}\_\{i\}=\\arg\\max q\_\{\\psi\}\(\\cdot\)\_\{i\}be the draft model’s current greedy token at positionii\(Figure[2](https://arxiv.org/html/2607.01893#S4.F2)\)\. AUF finds the first exact mismatch among valid positions,

j∗=min⁡\{j∈V:y^j≠yj\}\.j^\{\*\}=\\min\\\{j\\in V:\\hat\{y\}\_\{j\}\\neq y\_\{j\}\\\}\.If such a position exists, the active CE support isS=\{i∈V:i≤j∗\}S=\\\{i\\in V:i\\leq j^\{\*\}\\\}; otherwiseS=VS=V\. The loss is

ℒAUF=1\|S\|​∑i∈S−log⁡qψ​\(yi\)i\.\\mathcal\{L\}\_\{\\mathrm\{AUF\}\}=\\frac\{1\}\{\|S\|\}\\sum\_\{i\\in S\}\-\\log q\_\{\\psi\}\(y\_\{i\}\)\_\{i\}\.The first failing token is kept in the support because it is the decision that breaks the accepted prefix\. Tokens after the first failure are inactive because they would not be verified as accepted draft tokens in the corresponding SD iteration\. Equivalently, AUF replaces the fixed DFlash weightswiw\_\{i\}with the model\-dependent hard prefix weightai​\(ψ\)=𝟏​\[i≤j∗\]a\_\{i\}\(\\psi\)=\\mathbf\{1\}\[i\\leq j^\{\*\}\]\(withai=1a\_\{i\}=1for alliion a fully correct block\), so the loss is the weighted CE equation[1](https://arxiv.org/html/2607.01893#S2.E1)withci=ai​\(ψ\)c\_\{i\}=a\_\{i\}\(\\psi\)\. The maskai​\(ψ\)a\_\{i\}\(\\psi\)is computed from detached predictions and is not a gradient path: AUF remains a CE objective whose only change is the credit\-assignment rule over positions\.

#### What AUF gives up, and what it costs\.

Relative to the soft gate of equation[2](https://arxiv.org/html/2607.01893#S2.E2), the hard plug\-in discards two things\. First, it removes graded credit: a near\-miss at the breaker and a confidently correct early token both receive credit11, whereas the soft gate down\-weights a fragile prefix\. Second, a single deterministic argmax is a coarse,0/10/1estimator of the gate: on any given example the credit is binary rather than graded, so per\-example information about prefix confidence is lost\. These are exactly the two properties that D\-PACE’s smoothing and SpecDiff\-2’s product reward preserve at extra cost; AUF trades that graded information for a parameter\-free hard support\. What AUF buys in return is cost, simplicity, and one fewer inductive bias: it changes only the coefficientcic\_\{i\}in the existing decayed\-CE loss, needs only a detached greedy readout from the training logits to locatej∗j^\{\*\}, adds no auxiliary objective, samples no verifier trajectories, removes the decay hyperparameterγd\\gamma\_\{d\}, and leaves the inference pipeline and the rejection\-sampling exactness contract untouched\.

#### Two optimization axes\.

AUF changes training along two measurable axes\. First, it changes the*active token ratio*

ractive=\|S\|/B,r\_\{\\mathrm\{active\}\}=\|S\|/B,which measures how much of the block participates in the CE update: early in training the first error appears near the beginning, soractiver\_\{\\mathrm\{active\}\}is small, and as the drafter pushes the first failure rightward the support expands\. Second, it induces the diagnostic*support\-token accuracy*

asupport=1\|S\|​∑i∈S𝟏​\[y^i=yi\],a\_\{\\mathrm\{support\}\}=\\frac\{1\}\{\|S\|\}\\sum\_\{i\\in S\}\\mathbf\{1\}\[\\hat\{y\}\_\{i\}=y\_\{i\}\],measured on the same first\-error support that AUF selects for CE\. For AUF this is not an independent fixed\-denominator accuracy: because the support is the accepted prefix plus the breaker token, it is tied to the current first\-failure depth\. We use it as a training\-side diagnostic of where the support lies, and use common\-token accuracy and inference\-side conditional acceptance for fixed\-denominator comparisons\.

This exposes an optimization dimension that fixed\-support objectives — uniform CE, fixed decay, and dynamic reweighting such as D\-PACE — do not have: they keep the supervised token set fixed and improve only the accuracy or weighting of the same positions, whereas AUF can also improve by pushing the first failure later, growingractiver\_\{\\mathrm\{active\}\}\. AUF thus turns the left\-to\-right acceptance boundary itself into part of the training signal\. We read the resulting trajectory as an implicit easy\-to\-hard curriculum the drafter sets for itself: early on it is supervised to be reliable on a short accepted prefix \(smallractiver\_\{\\mathrm\{active\}\}\), and as that prefix competence grows it pushesj∗j^\{\*\}rightward and extends the supervised horizon with it, so a single driver moves both diagnostics up and to the right rather than two independently scheduled quantities \(Figure[3](https://arxiv.org/html/2607.01893#S4.F3)\)\. The native serving block size stays fixed; only the loss horizon grows, per example and per step, from the drafter’s realized prefix rather than a manually fixed block\-size schedule — mirroring the block\-diffusion observation that fine\-grained local correctness should be established before exploiting large parallel blocks\. This is an interpretation of the training dynamics measured in Section[5\.1](https://arxiv.org/html/2607.01893#S5.SS1), not a separate mechanism\.

![Refer to caption](https://arxiv.org/html/2607.01893v1/x3.png)Figure 3:A two\-dimensional training diagnostic over training steps, drawn schematically from the per\-step measurements of Figure[4](https://arxiv.org/html/2607.01893#S5.F4)\. Axes:x=x=active token ratioractive=\|S\|/Br\_\{\\mathrm\{active\}\}=\|S\|/B,y=y=accuracy on the selected first\-error supportasupporta\_\{\\mathrm\{support\}\}\. Dashed contours schematically indicate higher acceptance lengthτ\\tautoward the upper right\. A fixed\-support method moves almost vertically \(constantractiver\_\{\\mathrm\{active\}\}, accuracy measured on the same positions\)\. AUF instead traces an expanding\-support path where the active support grows as the first failurej∗j^\{\*\}moves rightward\.
#### AUF as a teacher\-forcing\-motivated support rule\.

Stated as interpretation rather than theorem, AUF is the loss\-side realization of the teacher\-forcing idea of Section[2](https://arxiv.org/html/2607.01893#S2)for drafters without an input\-side gold\-prefix channel\. The acceptance\-aware methods push back toward prefix\-sensitive supervision but mostly by reweighting a full\-block loss whose support still spans the block; each changes*how much*a position counts without changing*which*positions receive CE\. The first\-error focal objective even keys on the same breakerj∗j^\{\*\}yet*adds*a term on top of the full decayed CE, leaving the suffix supervised, whereas AUF setsci=0c\_\{i\}=0fori\>j∗i\>j^\{\*\}and*removes*it; among drafters, only Domino changes the conditioning event on the input side\. The analogy is intentionally limited: strict teacher forcing conditions on a*counterfactual*gold prefix, whereas AUF conditions the*support*on the drafter’s own realized greedy prefix up toj∗j^\{\*\}while the*target*at every supervised position stays the gold token\. We therefore use teacher\-forcing language as motivation, not as a claim that AUF exactly recovers the same conditional\.

#### Applying AUF to different drafters\.

For DFlash, AUF is applied directly to the block logits\. For Domino, which has a base branch and a final correction branch, the first\-error support is computed separately for each output distribution\. The change is scoped to the CE support and modifies neither the drafter architecture nor the inference\-time verifier contract\.

## 5Evaluation

#### Setup\.

We evaluate Qwen3\-8B drafters trained on ShareGPT\. The target model isQwen3\-8B\. We use the original ShareGPT training conversations directly, without regenerating assistant responses from the target model\. For Qwen3 we use the standardqwenchat template rather than the thinking\-enabledqwen3\-thinkingtemplate, so thinking is disabled both when formatting training data and when rendering evaluation prompts\. We treat thinking\-enabled Qwen3 as a different serving setting and do not vary it here\. DFlash uses a 5\-layer block drafter with target layers\{1,9,17,25,33\}\\\{1,9,17,25,33\\\}and block sizeB=16B=16; Domino uses the same backbone with its GRU\-prefix base/final two\-branch head\. Our baseline is the standard decayed\-CE configuration \(γ=7\\gamma=7\) recommended by the SpecForge training recipe\(Chenet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib7); Huanget al\.[2026](https://arxiv.org/html/2607.01893#bib.bib6)\); this is the default used in both DFlash and Domino and reproduces the exponential position decay adopted across the block\-drafter literature \(EAGLE\-3, DFlash, Domino all hand\-set an exponentialγ\\gamma\(Liet al\.[2025](https://arxiv.org/html/2607.01893#bib.bib5); Chenet al\.[2026](https://arxiv.org/html/2607.01893#bib.bib7); Huanget al\.[2026](https://arxiv.org/html/2607.01893#bib.bib6)\)\)\. AUF keeps the architecture and training data fixed and only changes the supervised support, replacing the full\-block decayed CE support with the first\-error support of Section[4](https://arxiv.org/html/2607.01893#S4)\. All decode numbers are produced by our SGLang DFlash/Domino V2 speculative\-decoding backend \(single GPU, batch size 1\) under two verification settings: greedy \(T=0T\{=\}0\) and sampling \(T=1T\{=\}1\); in both cases the draft proposal is greedy \(single top\-1 candidate per position\)\. Because every comparison in this section is*within*a fixed drafter architecture \(AUF is a training recipe, not a new model\), per\-iteration forward cost is identical across the variants we compare\. We therefore report average acceptance lengthτ\\tau\(mean accepted draft tokens plus one correction token per speculative iteration, as reported by SGLang’s built\-in metrics\) as the main decode metric throughout this section\.

#### Benchmarks\.

Both backbones are evaluated on the same six benchmarks: GSM8K, MATH\-500, HumanEval, MBPP, MT\-Bench, and Alpaca, with prompt counts 200, 200, 164, 200, 80, 200 and a uniformmax\_new\_tokens=512cap across all methods and temperatures\. Every drafter is trained for six epochs on ShareGPT; the decode tables report the epoch\-6 checkpoints, and the training\-dynamics figures use the full epoch\-1 optimizer\-step logs\. We separate the two backbones into their own subsections because the Domino two\-branch head admits a richer family of AUF variants\.

### 5\.1DFlash

DFlash has a single output distribution, so the AUF design space is small\. We train three matched variants: the official\-style*decay\-only*reference \(γ=7\\gamma=7full\-block CE\),*AUF\-only*\(first\-error truncated CE, no decay\), and*AUF\+decay*\(the same exponential decay applied*inside*the AUF support\)\. Table[2](https://arxiv.org/html/2607.01893#S5.T2)reports the epoch\-6 decode results\.

Table 2:DFlash epoch\-6 average acceptance length \(τ\\tau\) on Qwen3\-8B across six benchmarks, measured through the SGLang serving path \(batch size 1\)\. Best per temperature setting in bold\.Both AUF variants improve over the decay\-only reference on every benchmark under both greedy and sampling decoding \(Table[2](https://arxiv.org/html/2607.01893#S5.T2)\), with the largest gains on the longer, more structured code and math outputs; the sampling result confirms the gain is not an artifact of the greedy verification match used during training, and the advantage holds throughout training, not just at convergence \(Figure[4](https://arxiv.org/html/2607.01893#S5.F4)\)\. Notably,*AUF\-only and AUF\+decay are indistinguishable*: once the support is truncated at the first predicted error, re\-weighting the surviving positions with exponential decay adds nothing measurable\. We read this decay\-inert result in Section[6](https://arxiv.org/html/2607.01893#S6)\.

#### Training dynamics\.

Figure[4](https://arxiv.org/html/2607.01893#S5.F4)logs two token accuracies per optimizer step:*common\-token accuracy*, measured on a fixed common mask \(all natively\-valid block positions\) so the three methods share a denominator, and the*support accuracy*of Section[4](https://arxiv.org/html/2607.01893#S4), measured on the positions each method actually trains on \(for AUF, the selected first\-error support\)\. Two facts stand out\. First, on the common mask the*decay\-only*baseline is the*most*accurate, yet it is the*worst*at decode\. Second, AUF’s active token ratio starts low and grows over training while decay\-only trains the full block, so the AUF support diagnostic tracks a much shorter first\-error region\. This common\-mask accuracy inversion — more accurate yet slower — is the empirical signature we interpret in Section[6](https://arxiv.org/html/2607.01893#S6)\.

![Refer to caption](https://arxiv.org/html/2607.01893v1/x4.png)Figure 4:DFlash training dynamics across epochs \(rolling mean over30003000steps;τ\\taufrom six\-benchmark greedy SGLang decode\)\. Panels:\(1\)support accuracy, on the positions each method actually trains on \(for AUF, the selected first\-error support\);\(2\)common\-token accuracy, on the fixed common mask of all natively\-valid block positions;\(3\)active token ratio, the fraction of block positions each method supervises;\(4\)acceptance lengthτ\\tau\. See text for interpretation\.
#### Per\-position conditional acceptance\.

The matching inference\-side measurement is the per\-position*conditional*acceptance rateαk\\alpha\_\{k\}— among speculative steps whose draft prefix through positionk−1k\-1was fully accepted, the fraction that also accept positionkk,

αk=\#​\{A≥k\}\#​\{A≥k−1\},\\alpha\_\{k\}=\\frac\{\\\#\\\{A\\geq k\\\}\}\{\\\#\\\{A\\geq k\-1\\\}\},read off the accepted\-draft\-token histogram the SGLang verifier records per request\. This is exactly the per\-position factor in𝔼​\[τ\]=1\+∑k∏i≤kαi\\mathbb\{E\}\[\\tau\]=1\+\\sum\_\{k\}\\prod\_\{i\\leq k\}\\alpha\_\{i\}\(Section[2](https://arxiv.org/html/2607.01893#S2)\): it removes the compounding penalty of earlier rejections and isolates conditional predictive quality at each block offset\. We plot positions11–66only, where every curve retains a non\-trivial fraction of speculative steps in the conditioning set under the six\-benchmark average; deeper positions are too thin to be stable\. On DFlash \(Figure[5](https://arxiv.org/html/2607.01893#S5.F5), left\) both AUF variants lie above the decay\-only baseline across the block, and AUF\-only and AUF\+decay are again nearly indistinguishable: the decode gain is a lift of the conditional acceptance profile that determinesτ\\tau, not a global shift in raw token accuracy\.

![Refer to caption](https://arxiv.org/html/2607.01893v1/x5.png)Figure 5:Per\-position conditional acceptanceαk\\alpha\_\{k\}\(epoch 6, greedy SGLang decode\), averaged over all six benchmarks\. Aggregation weights prompts equally within each benchmark and then weights the six benchmarks equally; MT\-Bench’s two turns count as separate prompts\. Left: DFlash decay\-only, AUF\+decay, and AUF\-only\. Right: Domino decay\-only and the two base\-branch AUF variants \(B\-AUF\+D, B\-AUF\), using the same line styles\. AUF raises the six\-benchmark conditional acceptance profile on both backbones\.

### 5\.2Domino

Domino is harder to analyze because its head is not a single distribution: it mixes a*base*branch \(the drafter’s own logits\) and a*final*branch \(base plus a causal correction\), trained asL=λbase​Lbase\+\(1−λbase\)​LfinalL=\\lambda\_\{\\mathrm\{base\}\}L\_\{\\mathrm\{base\}\}\+\(1\-\\lambda\_\{\\mathrm\{base\}\}\)L\_\{\\mathrm\{final\}\}\. AUF therefore has a choice of*which support each branch trains on*, and there is no a\-priori “main” AUF line — we treat the branch\-support assignment as an experimental variable and let the measured decode decide\. We evaluate seven trained variants spanning that space \(Table[3](https://arxiv.org/html/2607.01893#S5.T3)\): three support assignments \(base\-only, base\-shared, branch\-specific\), each with and without theγ=7\\gamma=7decay applied inside the AUF support, plus the decay\-only baseline\.

Table 3:Domino AUF variants\. “Support” is the training mask used by each branch:common= full native block,base\-auf/final\-auf= first\-error truncation from the base/final branch\. Decay is theγ=7\\gamma=7position weight applied inside the support\. Short names are used in subsequent tables\.B= base\-only \(AUF on base branch only\);S= shared \(both branches share base\-auf support\);F= branch\-specific \(final branch uses its own final\-auf support\)\.\+D= decay applied inside the AUF support\.

Table 4:Domino epoch\-6 average acceptance length \(τ\\tau\) on Qwen3\-8B across six benchmarks, same SGLang protocol as Table[2](https://arxiv.org/html/2607.01893#S5.T2)\. Best per temperature block in bold; all AUF variants beat the decay\-only baseline\. Short names refer to Table[3](https://arxiv.org/html/2607.01893#S5.T3)\.Table[4](https://arxiv.org/html/2607.01893#S5.T4)shows the support\-selection idea transfers: every AUF variant beats the decay\-only baseline under both greedy and sampling decoding, regardless of how the two branches split their support\. Three observations sharpen the picture\.

First, the empirically strongest variant under greedy decoding is B\-AUF\+D, which applies AUF to the base branch, leaves the*final*branch on the common mask, and retains the decay inside the AUF support; under sampling, B\-AUF \(without decay\) is marginally stronger\. The gain is localized to the*base*\(proposer\) branch: its training loss drops sharply once AUF is applied, while pushing AUF onto the final branch as well does not help \(and slightly hurts\) — a degree of freedom DFlash’s single distribution does not expose\.

Second, the spread among the six AUF variants is small, so we report the ordering rather than claim a designed main line\. The smaller absolute Domino margin than on DFlash is consistent with its stronger baseline: a higher starting point leaves less headroom for support reshaping\.

Third, unlike DFlash where decay on top of AUF is inert \(Table[2](https://arxiv.org/html/2607.01893#S5.T2)\), on Domino decay adds a small benefit under greedy decoding across all three matched decay\-toggle pairs that vanishes or reverses under sampling\. The residual is modest and regime\-dependent; we take up whether it carries information beyond the support selection in Section[6](https://arxiv.org/html/2607.01893#S6)\.

#### Per\-position conditional acceptance on Domino\.

Domino’s two\-branch head has no single training\-accuracy axis to plot, so we read the effect of AUF off the inference side, with the sameαk\\alpha\_\{k\}used for DFlash \(Figure[5](https://arxiv.org/html/2607.01893#S5.F5), right\)\. The two base\-branch AUF variants \(B\-AUF and B\-AUF\+D\) lift the conditional acceptance profile over decay\-only through most of the block, but by a smaller margin than on DFlash, consistent with Domino’s stronger baseline and narrowτ\\tauspread\.

## 6Discussion

#### Why does AUF help?

AUF improvesτ\\tauover the decayed\-CE baseline across our runs \(Section[5](https://arxiv.org/html/2607.01893#S5)\)\. We are confident about the method’s structure and its train–inference\-consistency motivation \(Section[4](https://arxiv.org/html/2607.01893#S4)\), but not yet about the precise causal mechanism, which likely needs targeted interpretability analysis we leave to future work\. The principled explanation is that the full\-block CE supervises positions whose prefix the verifier never reaches, learning a target less prefix\-sensitive than inference itself, whereas AUF truncates the support at the first predicted failure and thus optimizes a quantity that tracks SGLang’s acceptance lengthτ\\taumore closely\. This is principled but not proven: “better aligned objective” and “higher measuredτ\\tau” are not the same statement, and we treat the causal link as a hypothesis\.

Two readings refine this\. The first is structural: AUF is a projection of an RL objective onto a supervised one\. Maximizing the verifier’s expected acceptance length𝔼​\[τ\]\\mathbb\{E\}\[\\tau\]would sample rollouts from the current policy, assign credit along them, and update with a reward\-weighted gradient; AUF keeps the on\-policy rollout \(the greedy block\) and the acceptance\-aligned credit rule \(the first\-error positionj∗j^\{\*\}deciding*where*to supervise\) but replaces the reward\-weighted policy gradient with the ordinary gold CE−∑i≤j∗∇ψlog⁡qψ,i​\(yi\)\-\\sum\_\{i\\leq j^\{\*\}\}\\nabla\_\{\\psi\}\\log q\_\{\\psi,i\}\(y\_\{i\}\)\. This explains the appeal — a stable dense CE gradient that still carries acceptance\-aligned credit — without our having measured that this is*why*it wins\. The second is a falsifiable prediction: supervising post\-failure positions is an off\-deployment task that competes for capacity with the early positions determining the accepted prefix, so fixed\-support baselines should buy higher generic token accuracy at the expense of decode\. This is exactly the inversion DFlash shows \(Section[5\.1](https://arxiv.org/html/2607.01893#S5.SS1)\); what it does not settle is whether the effect is causal data\-curation or the same inversion the consistency reading already predicts\.

#### A spectrum, with AUF as the minimal intervention\.

The existing objectives lie on one axis from supervised imitation toward verifier\-calibrated RL: uniform CE→\\toposition decay→\\toAUF→\\toD\-PACE→\\toSpecDiff\-2\. Uniform CE and fixed decay encode a position prior with no acceptance signal; AUF is the first point that conditions on the model’s realized prefix, using a hard on\-policy support and a gold target; D\-PACE softens the same gate into a graded weight; SpecDiff\-2 moves the target onto verifier trajectories, approaching the RL objective itself\(Sandleret al\.[2025](https://arxiv.org/html/2607.01893#bib.bib9)\)\. AUF is thus the*minimal*edit that conditions training on the realized accepted prefix, and is distinct from sequence\-level rejection\-sampling fine\-tuning: it performs block\-internal, token\-prefix\-level credit assignment tied to the left\-to\-right acceptance semantics of speculative decoding\.

#### One fewer inductive bias\.

A practical consequence is that AUF removes a hand\-designed component rather than adding one: it replaces the exponential position decay — a fixed, manually tuned weight — with the drafter’s own first\-failure boundary, which the DFlash result shows carries the same “earlier tokens matter more” prior*and*the acceptance signal the fixed prior lacks\. This removes the decay rateγd\\gamma\_\{d\}from the hyperparameter budget, and because the support is computed from the model rather than fixed ex ante, the rule is defined identically regardless of block sizeBBor backbone\. We stress this is a structural motivation, not an empirical scaling claim\.

#### Does AUF replace decay, or only supplement it?

On DFlash this is answered cleanly: AUF\-only and AUF\+decay are indistinguishable under both greedy and sampling decoding \(Section[5\.1](https://arxiv.org/html/2607.01893#S5.SS1)\), so decay is fully redundant once the support is selected\. On Domino a small greedy\-regime residual survives \(B\-AUF\+D2\.682\.68vs\. B\-AUF2\.662\.66\) but reverses under sampling \(B\-AUF2\.532\.53vs\. B\-AUF\+D2\.522\.52\); averaged across regimes the decay\-on and decay\-off variants are within noise and the sign flips with temperature\. We therefore conclude that decay is not a necessary complement to AUF on either backbone\.

#### Limitations\.

All results are at a single configuration: block sizeB=16B=16, target Qwen3\-8B, and ShareGPT training data\. Three axes remain unverified because each requires a full drafter retraining run\. We do not varyBBor model scale, so the broader\-default argument above is a structural expectation, not a confirmation; we do not include head\-to\-head retraining against D\-PACE or other acceptance\-aware baselines under matched compute; and whether AUF’s stable SFT\-side update is preferable to a tuned on\-policy RL objective, or only cheaper, is untested\.

## References

- Z\. An, T\. Liu, Z\. Liu, D\. Li, R\. Liu, and E\. Barsoum \(2026\)PARD\-2: target\-aligned parallel draft model for dual\-mode speculative decoding\.arXiv preprint arXiv:2605\.08632\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px2.p1.1)\.
- M\. Arriola, A\. Gokaslan, J\. T\. Chiu, Z\. Yang, Z\. Qi, J\. Han, S\. S\. Sahoo, and V\. Kuleshov \(2025\)Block diffusion: interpolating between autoregressive and diffusion language models\.InInternational Conference on Learning Representations,Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- C\. Chen, S\. Borgeaud, G\. Irving, J\. Lespiau, L\. Sifre, and J\. Jumper \(2023\)Accelerating large language model decoding with speculative sampling\.arXiv preprint arXiv:2302\.01318\.Cited by:[§1](https://arxiv.org/html/2607.01893#S1.p1.1)\.
- J\. Chen, Y\. Liang, and Z\. Liu \(2026\)DFlash: block diffusion for flash speculative decoding\.arXiv preprint arXiv:2602\.06036\.Note:Accepted at ICML 2026Cited by:[§1](https://arxiv.org/html/2607.01893#S1.p2.1),[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px2.p1.1),[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1),[§5](https://arxiv.org/html/2607.01893#S5.SS0.SSS0.Px1.p1.7)\.
- L\. Hu, Z\. Feng, Y\. Wu, H\. Yuan, Y\. Zhao, Y\. Qian, B\. Wang, P\. Zhao, D\. Jiang, Y\. Zhu, T\. Rosing, and H\. Zhang \(2026\)JetSpec: breaking the scaling ceiling of speculative decoding with parallel tree drafting\.arXiv preprint arXiv:2606\.18394\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- S\. Hu, J\. Li, X\. Xie, Z\. Lu, K\. Toh, and P\. Zhou \(2025\)GRIFFIN: effective token alignment for faster speculative decoding\.arXiv preprint arXiv:2502\.11018\.Cited by:[§1](https://arxiv.org/html/2607.01893#S1.p4.1),[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px1.p1.5)\.
- J\. Huang, Y\. Zhang, Q\. Zhang, H\. Lin, H\. Xu, and L\. Zhang \(2026\)Domino: decoupling causal modeling from autoregressive drafting in speculative decoding\.arXiv preprint arXiv:2605\.29707\.Cited by:[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px5.p1.3),[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1),[§5](https://arxiv.org/html/2607.01893#S5.SS0.SSS0.Px1.p1.7)\.
- F\. Huszár \(2015\)How \(not\) to train your generative model: scheduled sampling, likelihood, adversary?\.arXiv preprint arXiv:1511\.05101\.Cited by:[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px5.p1.3)\.
- Y\. Leviathan, M\. Kalman, and Y\. Matias \(2023\)Fast inference from transformers via speculative decoding\.InInternational Conference on Machine Learning,Cited by:[§1](https://arxiv.org/html/2607.01893#S1.p1.1)\.
- Y\. Li, F\. Wei, C\. Zhang, and H\. Zhang \(2025\)EAGLE\-3: scaling up inference acceleration of large language models via training\-time test\.arXiv preprint arXiv:2503\.01840\.Cited by:[§1](https://arxiv.org/html/2607.01893#S1.p3.2),[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px5.p1.3),[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px4.p1.1),[§5](https://arxiv.org/html/2607.01893#S5.SS0.SSS0.Px1.p1.7)\.
- M\. Nistor \(2026\)Halfway speculative decoding: direct acceptance rate optimization with joint drafter\-target training\.Note:Technical report,https://sergiu\-nistor\.com/assets/publications/Halfway\_Speculative\_Decoding\.pdfCited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px2.p1.1)\.
- S\. S\. Sahoo, M\. Arriola, Y\. Schiff, A\. Gokaslan, E\. Marroquin, J\. T\. Chiu, A\. Rush, and V\. Kuleshov \(2024\)Simple and effective masked diffusion language models\.InAdvances in Neural Information Processing Systems,Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- A\. Samarin, S\. Krutikov, A\. Shevtsov, S\. Skvortsov, F\. Fisin, and A\. Golubev \(2026\)LK losses: direct acceptance rate optimization for speculative decoding\.arXiv preprint arXiv:2602\.23881\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px2.p1.1)\.
- J\. Sandler, J\. K\. Christopher, T\. Hartvigsen, and F\. Fioretto \(2025\)SpecDiff\-2: scaling diffusion drafter alignment for faster speculative decoding\.arXiv preprint arXiv:2511\.00606\.Cited by:[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px3.p1.1),[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px4.p1.8),[§6](https://arxiv.org/html/2607.01893#S6.SS0.SSS0.Px2.p1.4)\.
- Y\. Tian, Y\. Liang, S\. Zhang, Y\. Shu, G\. Yang, W\. He, S\. Fang, T\. Guo, K\. Han, C\. Xu, H\. Chen, X\. Chen, and Y\. Wang \(2025\)From next\-token to next\-block: a principled adaptation path for diffusion LLMs\.arXiv preprint arXiv:2512\.06776\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- Y\. Wang, L\. Yang, B\. Li, Y\. Tian, K\. Shen, and M\. Wang \(2025\)Revolutionizing reinforcement learning framework for diffusion large language models\.arXiv preprint arXiv:2509\.06949\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- L\. Whalen, Y\. Ito, and R\. Sakamoto \(2026\)Teaching diffusion to speculate left\-to\-right\.arXiv preprint arXiv:2606\.11552\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px1.p1.5)\.
- T\. Wu, Y\. Yao, Z\. Qi, H\. Zheng, Z\. Wang, H\. Ma, L\. Liao, H\. Lakkaraju, J\. Li, and Y\. Du \(2026a\)D\-PACE: dynamic position\-aware cross\-entropy for parallel speculative drafting\.arXiv preprint arXiv:2605\.18810\.Cited by:[§1](https://arxiv.org/html/2607.01893#S1.p4.1),[§1](https://arxiv.org/html/2607.01893#S1.p5.1),[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px4.p1.4),[§2](https://arxiv.org/html/2607.01893#S2.SS0.SSS0.Px4.p1.8),[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px1.p1.5)\.
- Z\. Wu, L\. Zheng, J\. Ye, S\. Gong, X\. Zhao, Y\. Feng, W\. Bi, and L\. Kong \(2026b\)DreamReasoner\-8B: block\-size curriculum learning for diffusion reasoning models\.arXiv preprint arXiv:2606\.19257\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- L\. Zhang, J\. Zhang, J\. Yao, R\. Yan, Y\. Yang, J\. Zhang, T\. Yang, Y\. Wu, and B\. Yuan \(2026a\)D2SD: accelerating speculative decoding with dual diffusion draft models\.arXiv preprint arXiv:2606\.04446\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- Y\. Zhang, S\. Chen, H\. Ye, and E\. Feng \(2026b\)HCSpec: two\-tier horizontal cascade speculative decoding for high\-efficiency large language model inference\.InProceedings of the 64th Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),pp\. 7773–7783\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px3.p1.1)\.
- X\. Zou, J\. Li, J\. Huang, and P\. Zhou \(2026\)Variational speculative decoding: rethinking draft training from token likelihood to sequence acceptance\.arXiv preprint arXiv:2602\.05774\.Cited by:[§3](https://arxiv.org/html/2607.01893#S3.SS0.SSS0.Px2.p1.1)\.