BV Loss: Block Verification-Aware Loss for Block Diffusion Speculative Decoding

Suyoung Kim; Jahyun Koo; Hyeonjin Kim; Inhyeok Bang; Seunghyun Lee; Hyunjae Oh; Baeseong Park; Dongsoo Lee

cs.AISep 28, 2026

BV Loss: Block Verification-Aware Loss for Block Diffusion Speculative Decoding

Authors: Suyoung Kim, Jahyun Koo, Hyeonjin Kim, Inhyeok Bang, Seunghyun Lee, Hyunjae Oh, Baeseong Park, Dongsoo Lee

Organizations: a2sys (a2sys.ai) · Seoul National University (snu.ac.kr) · University of Wisconsin (wisc.edu)

Abstract

Diffusion drafters accelerate speculative decoding by proposing multiple tokens in parallel. Despite recent advances in speculative decoding through sequence-level drafting and verification, existing training objectives remain largely designed around token-level verification. To address this mismatch, we introduce Block Verification-aware loss (BV loss), a training objective designed to maximize the expected acceptance length of a drafted sequence. BV loss is directly derived from the block verification acceptance rule, providing a principled connection between the drafter training objective and the inference-time verification mechanism at the sequence level. Across math, code, and chat benchmarks, BV loss increases the mean number of tokens accepted per verification call under block verification by 13.0--21.0% over cross-entropy loss training for DFlash and DSpark with Qwen3-4B and Qwen3-8B without changing the inference procedure. BV loss also outperforms tokenwise acceptance objectives such as TV loss and LK loss, and its gains extend to token verification and greedy decoding. These results demonstrate the benefit of training block diffusion drafters with an objective aligned with sequence-level verification, rather than optimizing each token independently.

Figures & tables

Drafter loss	Training objective	Uses teacher probabilities?	Verification- aware?	Block- aware?
CE	Maximize log-likelihood	✗	✗	✗
KL / RKL	Minimize KL divergence	✓	✗	✗
TV	Maximize token acceptance	✓	✓	✗
$\mathrm{LK}$	Maximize token acceptance	✓	✓	✗
BV (Ours)	Maximize block acceptance length	✓	✓	✓

Table 1: Comparison of drafter training objectives. CE and KL / RKL optimize token likelihood or distribution matching, whereas TV and LK loss explicitly target token-level acceptance. BV loss is instead derived from block verification and directly optimizes the expected accepted draft length, making it both verification-aware and block-aware.

		$T=0$ (greedy)				$T=1$ (block verification)
		DFlash		DSpark		DFlash		DSpark
Target	Loss	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup
Qwen3-4B	CE	4.65	3.71 $\times$	5.21	3.97 $\times$	4.09	3.21 $\times$	4.77	3.47 $\times$
	KL	4.80	3.76 $\times$	5.49	4.15 $\times$	4.17	3.23 $\times$	4.97	3.67 $\times$
	RKL	4.05	3.24 $\times$	4.87	3.73 $\times$	3.87	3.09 $\times$	4.68	3.45 $\times$
	TV	1.98	1.60 $\times$	2.23	1.74 $\times$	1.96	1.57 $\times$	2.21	1.66 $\times$

Table 2: Average performance over seven benchmarks on Qwen3-4B and Qwen3-8B under greedy decoding (

T=0

) and block verification (

T=1

). Average acceptance length

\tau

includes correction/bonus tokens. Speedup is relative to autoregressive decoding. Boldface indicates the best average in each column within each target.

Target	Drafter	$\tau$ under token verification
Target	Drafter	CE	KL	RKL	TV	LK	BV (Ours)
Qwen3-4B	DFlash	4.01	4.11	3.86	1.96	4.17	4.85
Qwen3-4B	DSpark	4.64	4.84	4.64	2.20	4.98	5.20
Qwen3-8B	DFlash	4.04	4.13	3.00	1.01	4.19	4.86
Qwen3-8B	DSpark	4.63	4.90	3.38	1.02	5.05	5.26

Table 3: Generalization to token verification at

T=1

with the same checkpoints as Table 2 . Entries are seven-benchmark mean

\tau

, using the same counting convention. Bold marks the best mean in each row, including ties.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

	Qwen3-4B				Qwen3-8B
	DFlash		DSpark		DFlash		DSpark
Training loss	$T=0$	$T=1$	$T=0$	$T=1$	$T=0$	$T=1$	$T=0$	$T=1$
Baseline (CE)	4.65	4.09	5.21	4.77	4.64	4.15	5.10	4.71
BV w/o annealing	4.98	4.74	5.37	5.17	5.07	4.80	5.36	5.13
BV with annealing (Ours)	5.22	4.95	5.62	5.39	5.27	4.98	5.67	5.43

Appendix

Table 4: BV and annealing ablation. Entries are average

\tau

over the seven benchmarks, with the counting convention of Table 2 . At

T=1

, both drafters use block verification.

Drafter	Loss	Math						Code						Chat
Drafter	Loss	GSM8K		MATH-500		AIME25		HumanEval		MBPP		LCB		MT-Bench		Avg.
$T=0$		Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$
DFlash	CE	4.99 $\times$	6.32	4.46 $\times$	5.64	3.63 $\times$	4.50	3.53 $\times$	4.45	3.41 $\times$	4.27	3.59 $\times$	4.44	2.34 $\times$	2.94	3.71 $\times$	4.65
	KL	5.05 $\times$	6.51	4.54 $\times$	5.83	3.68 $\times$	4.67	3.60 $\times$	4.61	3.46 $\times$	4.40	3.61 $\times$	4.56	2.40 $\times$	3.03	3.76 $\times$	4.80
	RKL	4.52 $\times$	5.69	3.84 $\times$	4.81	3.09 $\times$	3.85	3.05 $\times$	3.82	2.99 $\times$	3.71	3.22 $\times$	3.98	2.00 $\times$	2.51	3.24 $\times$	4.05
	TV	1.95 $\times$	2.42	2.01 $\times$	2.48	1.78 $\times$	2.19	1.39 $\times$	1.71	1.44 $\times$	1.77	1.34 $\times$	1.63	1.32 $\times$	1.64	1.60 $\times$	1.98

Appendix

Table 5: Full benchmark results for DFlash and DSpark on Qwen3-4B. Here,

\tau

is the reported verification-call length, including correction/bonus when present; the Method uses draft-only

\tau

. Avg. retains the reported seven-benchmark mean. Speedup is relative to autoregressive decoding. Bold marks the best value for each metric within each drafter and setting..

Drafter	Loss	Math						Code						Chat
Drafter	Loss	GSM8K		MATH-500		AIME25		HumanEval		MBPP		LCB		MT-Bench		Avg.
$T=0$		Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$	Speedup	$\tau$
DFlash	CE	4.70 $\times$	6.11	4.28 $\times$	5.57	3.53 $\times$	4.55	3.54 $\times$	4.61	3.26 $\times$	4.20	3.58 $\times$	4.58	2.32 $\times$	2.88	3.60 $\times$	4.64
	KL	4.86 $\times$	6.37	4.42 $\times$	5.79	3.59 $\times$	4.67	3.69 $\times$	4.80	3.37 $\times$	4.34	3.67 $\times$	4.72	2.39 $\times$	2.97	3.71 $\times$	4.81
	RKL	2.95 $\times$	3.82	2.80 $\times$	3.63	2.34 $\times$	3.01	2.33 $\times$	3.03	2.34 $\times$	3.01	2.44 $\times$	3.11	1.71 $\times$	2.12	2.42 $\times$	3.10
	TV	0.81 $\times$	1.02	0.81 $\times$	1.01	0.80 $\times$	1.01	0.80 $\times$	1.00	0.79 $\times$	1.01	0.82 $\times$	1.01	0.82 $\times$	1.01	0.81 $\times$	1.01

Appendix

Table 6: Full benchmark results for DFlash and DSpark on Qwen3-8B. Here,

\tau

is the reported verification-call length, including correction/bonus when present; the Method uses draft-only

\tau

. Avg. retains the reported seven-benchmark mean. Speedup is relative to autoregressive decoding. Bold marks the best value for each metric within each drafter and setting.

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Ceiling-Clipped Acceptance Histograms Indicate Stranded Speed-up in Block-Diffusion Speculative Decoding

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Advanced Micro Devices, Inc., USA

Block-Diffusion Drafter Drafter Speculative Decoding Decode Speedup Diffusion Language Models Continuation+1

Open paper AskPDF arXiv

Speculative decoding speeds up generation with an efficient draft model (drafter) that proposes tokens for a target model to verify in one pass, preserving the target's output distribution. High-acceptance block-diffusion drafters such as DFlash and DFlare fill an entire block in one parallel pass. In many cycles, the target accepts the whole block, so the drafter exhausts its trained block horizon before verification fails. We call this unrealized acceptance stranded speed-up. A mean committed length, per prompt or per cycle, hides it, whereas the acceptance histogram exposes it as a spike in the ceiling bin, the fraction of cycles that accept the entire block. We recommend the histogram as a preflight check before spending training compute. Naively widening the block at inference does not recover the speed-up, because once the block outgrows its training size, the drafter's bidirectional attention shifts its distribution even at early positions and erodes front-of-block verification. Instead, we post-train the drafter on a longer block with a short curriculum that emphasizes the newly exposed positions, a method we call DBloom. Expanding the pretrained DFlash and DFlare drafters from block size 16 to 24 across Qwen3-8B and Qwen3-4B targets raises the per-prompt committed length on the high-ceiling benchmarks by a median of +0.8 tokens (up to +1.1). Once continuation fine-tuning precedes expansion, the increase reaches 1.37 tokens. The same expansion also lifts committed length on all seven benchmarks for Gemma-4-12B-IT, a different model family, by a median of +0.41 tokens (Arm A), and the full continuation-then-expand pipeline (Arm B) adds +0.29 to +0.98 tokens over the same B16 drafter. In a prompt-matched comparison against JetSpec, a contemporary tree-based drafter not used in our design, DBloom commits more tokens on every benchmark at tree budgets up to 64 nodes.

Abstract

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