On the SPOT: Enhancing Speculative Decoding for Diffusion Language Models via Commit-Order Prediction

Eliezer Shlomi; Eliron Rahimi; Avi Mendelson; Chaim Baskin

cs.LGOct 15, 2026

On the SPOT: Enhancing Speculative Decoding for Diffusion Language Models via Commit-Order Prediction

Authors: Eliezer Shlomi, Eliron Rahimi, Avi Mendelson, Chaim Baskin

Organizations: Technion – Israel Institute of Technology · INSIGHT Lab, School of Electrical and Computer Engineering, Ben-Gurion University of the Negev

Abstract

Diffusion language models (DLMs) promise parallel text generation, but in practice face an unresolved speed-quality trade-off. Exact decoding fills in only one masked position per model pass, while faster multi-token decoding schemes are lossy. Speculative decoding is the standard lossless acceleration for autoregressive models. However, it does not transfer directly to DLMs, which must choose both what to generate and where. We show that this order is the missing piece: the model's own predictions from the previous pass already give the right token at 92-100% of positions, but not which position comes next. Based on this observation, we introduce Speculating Positions Order Trajectory (SPOT), which learns to predict this order. A 0.62M-parameter model reads only the target's output distributions and proposes a tree of candidate continuations, and the target verifies all of them in a single pass by checking whether each equals its own next state. On the verification side, our analysis shows that prior block-diffusion verification approaches either assume $T=0$ or a sequential proposal interface. To support tree-based speculation at any temperature, we propose using coupled-noise match verification for diffusion blocks, following shared-Gumbel-noise coupling approaches. Our comprehensive experiments show that SPOT cuts target passes by up to 6.8x and reaches up to 3.2x the throughput of standard decoding, beating the calibrated and training-free drafting baselines in every task and budget at $T=0$ and $T=1$ . In addition, we show that the learned drafter transfers across models, demonstrating successful transfer across six different DLMs. Project page: https://eliezer318.github.io/SPOT-dLLM/

Figures & tables

Figure 1: SPOT overview (red: committed; amber dashed: drafted; grey: masked, with its stale argmax token). (a) The target commits its most confident position per forward: the tokens are largely known in advance, the order is not. (b) SPOT reads a hypothetical prefix’s stale distributions, predicts the next position with a

0.62

M order model, grows a tree of states by prefix mass (edge width), and verifies all of them in one batched forward, committing three positions.

Figure 2: (a) Live oracle ceilings on SDAR-8B (b32): peak throughput ratios over draft-free decoding; positions are worth more than tokens, and a perfect drafter reaches

3.8

–

4.6\times

(full grid in Table 7 ). (b) Stale coverage : probability that all committed tokens over the next

K

steps lie within the stale top-

t

candidates.

	draft-free ( $D0$ )			SPOT $D8$ NFE (tok/s ratio)			greedy SPOT		Spiffy $D8$ NFE
$T$	acc	argmax	mean $p$	coupled	uncoupled	greedy †	acc	argmax	coupled	uncoupled
0.5	0.35	0.986	0.993	58.2 (2.56)	58.2 (2.57)	57.6 (2.57)	0.36	0.978	84.3	84.0
1.0	0.34	0.976	0.965	60.1 (2.45)	60.2 (2.43)	56.8 (2.55)	0.38	0.973	86.3	86.6
1.5	0.08	0.866	0.828	74.0 (1.97)	82.6 (1.77)	57.4 (2.55)	0.28	0.958	94.2	108.9
2.0	0.00	0.057	0.052	187.4 (0.78)	256.7 (0.54)	94.7 (1.52)	0.01	0.750	114.6	258.5
2.5	0.00	0.001	0.000	200.8 (0.71)	269.1 (0.54)	128.1 (1.13)	0.00	0.582	110.5	269.2

Table 1: Temperature sweep on SDAR-8B MBPP. Draft-free columns: target accuracy, argmax fraction, mean committed-token probability. SPOT

D8

: NFE and throughput against the

T

-matched draft-free control. Greedy-match columns show distribution drift. The

D8

NFE standard deviation over seeds grows from

0.3

T{=}0.5

8.5

T{=}2.5

. † Greedy match is not distribution-preserving, so its NFE is not comparable.

NFE $\downarrow$ ( tok/s $\uparrow$ )	GSM8K		MBPP		HumanEval		MATH500
method	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
$T{=}0$	acc. 0.89–0.90		acc. 0.41–0.43		acc. 0.74–0.74		acc. 0.11–0.11
no draft ( $D0$ )	270.8 $\downarrow$ ( 1.00 $\uparrow$ )		269.2 $\downarrow$ ( 1.00 $\uparrow$ )		271.4 $\downarrow$ ( 1.00 $\uparrow$ )		271.8 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	69.6 ( 2.50 )	52.6 ( 1.56 )	56.7 ( 2.61 )	39.6 ( 1.72 )	62.2 ( 2.74 )	44.6 ( 1.85 )	84.5 ( 2.03 )	66.0 ( 1.20 )
SPOT- $\gamma$ (ours)	75.1 ( 2.76 )	67.8 ( 2.78 )	60.7 ( 2.98 )	47.8 ( 2.99 )	66.5 ( 3.09 )	56.4 ( 3.13 )	92.2 ( 2.27 )	89.5 ( 2.27 )
Spiffy graph	91.3 ( 1.96 )	71.9 ( 1.14 )	83.4 ( 1.86 )	61.3 ( 1.17 )	86.8 ( 2.11 )	65.9 ( 1.28 )	99.4 ( 1.80 )	82.7 ( 0.99 )

Table 2: Main results, SDAR-8B b32 at

T{=}0

and

T{=}1

: NFE per sample ( throughput ratio over the shared draft-free control), best in bold, second best underlined. Shaded rows give each block’s accuracy range. SPOT-

\gamma

: unpadded,

\gamma{=}0.1

. At

T{=}1

all methods use coupled-noise match except the free chain (RS). Over seeds the ratio’s standard deviation is at most

0.15

and NFE’s at most

1.3

NFE $\downarrow$ at $D8$	GSM8K		MBPP		HumanEval		MATH500
target $\backslash$ drafter	SDAR-8B	mini	SDAR-8B	mini	SDAR-8B	mini	SDAR-8B	mini
SDAR-8B	69.6	72.8	56.7	58.6	62.2	66.8	84.5	87.9
LLaDA2.0-mini	85.9	83.0	105.2	94.9	97.8	88.2	87.1	84.8
LLaDA-8B †	79.8	83.1	54.5	56.7	83.3	87.6	83.6	86.3
Dream-7B †	66.0	67.8	51.2	52.0	57.3	58.3	77.2	79.1

Table 3: Checkpoint transfer (

T{=}0

, b32,

D8

, padded): each checkpoint pointed at a target with no retraining or recalibration, NFE per sample , the better drafter in bold. Both drafters run the same target weights over the same

(1{+}D)L

positions per forward, so throughput tracks NFE (ratios in Table 14 ). † approximate prefix cache of Wu et al. (2026) , not distribution-preserving.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

target	$\gamma{=}0$	$0.02$	$0.05$	$0.1$	$0.2$
SDAR-8B b32	2.58	3.01	3.21	3.53	3.38
SDAR-4B b32	2.99	3.54	3.63	3.62	3.46
LLaDA2.0-mini b32	2.10	2.09	2.04	1.94	1.94

Appendix

Table 4: Mass-floor calibration grids: mean throughput ratio over

D8/D12/D20

on the

50

held-out MBPP samples, unpadded, against the same card’s draft-free run. Bold: selected.

target	method	GSM8K	MATH500	HumanEval	MBPP
SDAR-1.7B	MRP (reported)	$1.25\times$	$1.23\times$	$1.23\times$	$1.17\times$
SDAR-1.7B	SPOT (ours)	$\mathbf{2.79\times}$ (3.6)	$\mathbf{2.49\times}$ (3.2)	$\mathbf{3.15\times}$ (4.2)	$\mathbf{3.61\times}$ (4.9)
SDAR-4B	MRP (reported)	$1.36\times$	$1.26\times$	$1.35\times$	$1.27\times$
SDAR-4B	SPOT (ours)	$\mathbf{3.17\times}$ (4.0)	$\mathbf{2.63\times}$ (3.3)	$\mathbf{3.48\times}$ (4.4)	$\mathbf{3.48\times}$ (4.9)
SDAR-8B	MRP (reported)	$1.40\times$	$1.39\times$	$1.34\times$	$1.34\times$
SDAR-8B	SPOT (ours)	$\mathbf{2.50\times}$ (3.9)	$\mathbf{2.03\times}$ (3.2)	$\mathbf{2.74\times}$ (4.4)	$\mathbf{2.61\times}$ (4.7)

Appendix

Table 5: MRP’s reported speedups next to SPOT. MRP: speculative mode (

K{=}3

) over its one-token-per-step baseline, Table 2 of Xu et al. (2026) (one H100, block width

16

, greedy). SPOT:

D8

throughput ratio over our draft-free control (block width

32

, length

256

, one RTX 6000 Ada), NFE reduction in parentheses. MRP generates up to

4096

tokens. Different implementations: relative gains only.

method	drafter	size	learns order	multi-step	exact $T{>}0$	single device
Spiffy ( 2026 )	offline graph	—	✗	✓	✗	✓
SSD ( 2025 )	self (confidence)	—	✗	✓	✗	✓
BlockSpec ( 2025 )	self (conf. tree)	—	✗	✓	✗	✓
SimSD ( 2026 )	sibling model	1.7B	✓	✓	approx.	✗
MRP ( 2026 )	residual head	3 layers	✗	✓	✗	✓
SPOT (ours)	order model	0.62M	✓	✓	✓	✓

Appendix

Table 6: Speculative decoding for diffusion targets, on the axes this paper argues are the relevant ones. “Learns order” = the commit order is predicted by a trained model rather than read off stale confidence or fixed offline; “multi-step” = one drafted proposal spans more than one commit; “exact

T{>}0

” = the committed distribution is provably the target’s at sampling temperature.

			position oracle			token oracle			joint oracle
setting	metric	draft-free	$D8$	$D12$	$D20$	$D8$	$D12$	$D20$	$D8$	$D12$	$D20$
SDAR-8B b32 GSM8K	NFE	271.1	50.1 (5.4 $\times$ )	43.0 (6.3 $\times$ )	38.2 (7.1 $\times$ )	68.6 (3.9 $\times$ )	64.8 (4.2 $\times$ )	62.1 (4.4 $\times$ )	46.8 (5.8 $\times$ )	38.2 (7.1 $\times$ )	31.3 (8.7 $\times$ )
SDAR-8B b32 GSM8K	tok/s ratio	18.4 tok/s	3.89 $\times$	4.02 $\times$	3.25 $\times$	2.81 $\times$	2.60 $\times$	1.89 $\times$	4.19 $\times$	4.56 $\times$	4.02 $\times$
SDAR-8B b32 MBPP	NFE	267.1	46.8 (5.7 $\times$ )	39.7 (6.7 $\times$ )	33.0 (8.1 $\times$ )	53.7 (5.0 $\times$ )	47.2 (5.7 $\times$ )	40.9 (6.5 $\times$ )	43.7 (6.1 $\times$ )	35.4 (7.5 $\times$ )	27.5 (9.7 $\times$ )
SDAR-8B b32 MBPP	tok/s ratio	18.7 tok/s	3.25 $\times$	3.36 $\times$	3.05 $\times$	2.82 $\times$	2.77 $\times$	2.35 $\times$	3.50 $\times$	3.77 $\times$	3.53 $\times$
SDAR-8B b32 HumanEval	NFE	272.6	47.5 (5.7 $\times$ )	40.0 (6.8 $\times$ )	33.4 (8.2 $\times$ )	62.3 (4.4 $\times$ )	57.6 (4.7 $\times$ )	53.6 (5.1 $\times$ )	46.1 (5.9 $\times$ )	37.9 (7.2 $\times$ )	30.3 (9.0 $\times$ )

Appendix

Table 7: Live-oracle grid,

T{=}0

, generation length 256,

n{=}100

, seed 0. Per setting: NFE (reduction

\times

over the setting’s draft-free NFE) and honest tok/s ratio over the setting’s draft-free throughput, for the position, token and joint oracles at

D8

D12

D20

; the draft-free column gives the baseline NFE and tok/s. Bold: best NFE and best throughput per setting.

NFE $\downarrow$ ( tok/s $\uparrow$ )	GSM8K		MBPP		HumanEval		MATH500
	acc. 0.86–0.87		acc. 0.25–0.26		acc. 0.59–0.60		acc. 0.13–0.14
method	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
no draft ( $D0$ )	270.8 $\downarrow$ ( 1.00 $\uparrow$ )		269.2 $\downarrow$ ( 1.00 $\uparrow$ )		271.4 $\downarrow$ ( 1.00 $\uparrow$ )		271.8 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	68.4 ( 3.17 )	51.2 ( 2.25 )	54.6 ( 3.48 )	37.9 ( 2.26 )	61.5 ( 3.48 )	44.9 ( 2.51 )	82.2 ( 2.63 )	64.7 ( 1.73 )
SPOT- $\gamma$ (ours)	68.5 ( 3.12 )	53.1 ( 3.04 )	54.9 ( 3.69 )	39.9 ( 3.34 )	61.8 ( 3.34 )	46.1 ( 3.28 )	82.4 ( 2.72 )	68.3 ( 2.38 )
Spiffy graph	91.1 ( 2.71 )	71.3 ( 1.77 )	82.5 ( 2.52 )	59.8 ( 1.54 )	88.6 ( 2.69 )	66.6 ( 1.81 )	97.6 ( 2.50 )	80.5 ( 1.54 )

Appendix

Table 8: Main results, SDAR-4B b32,

T{=}0

(format as Table 2 ). SPOT has the lowest NFE and the highest throughput ratio in every ours-vs-baseline comparison. The ratio’s standard deviation over seeds is at most

0.24

NFE $\downarrow$ ( tok/s $\uparrow$ )	GSM8K		MBPP		HumanEval		MATH500
	acc. 0.86–0.88		acc. 0.19–0.23		acc. 0.56–0.60		acc. 0.14–0.16
method	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
no draft ( $D0$ )	270.8 $\downarrow$ ( 1.00 $\uparrow$ )		269.2 $\downarrow$ ( 1.00 $\uparrow$ )		271.4 $\downarrow$ ( 1.00 $\uparrow$ )		271.8 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	71.0 ( 3.01 )	53.4 ( 2.26 )	57.0 ( 3.35 )	40.2 ( 2.17 )	63.0 ( 3.47 )	46.2 ( 2.45 )	86.0 ( 2.53 )	68.2 ( 1.71 )
SPOT- $\gamma$ (ours)	71.5 ( 3.14 )	56.0 ( 3.06 )	57.9 ( 3.44 )	42.9 ( 3.24 )	63.1 ( 3.56 )	48.1 ( 3.31 )	86.7 ( 2.60 )	72.6 ( 2.27 )
Spiffy graph	94.0 ( 2.60 )	74.4 ( 1.81 )	85.0 ( 2.47 )	62.9 ( 1.50 )	90.3 ( 2.75 )	68.3 ( 1.85 )	102.5 ( 2.40 )	86.4 ( 1.48 )

Appendix

Table 9: SDAR-4B b32 at

T{=}1

(coupled-noise match; free chain also under rejection sampling). Every comparison won on both columns. Over seeds the ratio’s standard deviation is at most

0.16

and NFE’s at most

0.6

NFE $\downarrow$ ( tok/s $\uparrow$ )	GSM8K		MBPP		HumanEval		MATH500
	acc. 0.70–0.72		acc. 0.27–0.31		acc. 0.45–0.47		acc. 0.09–0.10
method	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
no draft ( $D0$ )	270.8 $\downarrow$ ( 1.00 $\uparrow$ )		269.2 $\downarrow$ ( 1.00 $\uparrow$ )		271.4 $\downarrow$ ( 1.00 $\uparrow$ )		271.8 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	75.5 ( 2.79 )	58.8 ( 2.87 )	55.4 ( 3.61 )	38.9 ( 3.34 )	64.6 ( 3.15 )	46.4 ( 3.26 )	85.1 ( 2.49 )	67.7 ( 2.51 )
SPOT- $\gamma$ (ours)	75.9 ( 2.95 )	62.2 ( 3.40 )	55.7 ( 3.74 )	40.5 ( 4.48 )	64.7 ( 3.24 )	48.2 ( 4.04 )	85.3 ( 2.50 )	71.7 ( 2.82 )
Spiffy graph	94.0 ( 2.63 )	76.8 ( 2.93 )	84.5 ( 2.87 )	64.4 ( 2.58 )	89.2 ( 2.69 )	69.4 ( 3.09 )	98.6 ( 2.51 )	82.8 ( 2.64 )

Appendix

Table 10: Main results, SDAR-1.7B b32,

T{=}0

(format as Table 2 ). SPOT has the lowest NFE in every ours-vs-baseline comparison and the higher throughput ratio in

21

24

; SPOT-

\gamma

, which drops the padding, leads in

23

. The ratio’s standard deviation over seeds is at most

0.17

NFE $\downarrow$ ( tok/s $\uparrow$ )	GSM8K		MBPP		HumanEval		MATH500
	acc. 0.69–0.71		acc. 0.23–0.28		acc. 0.37–0.40		acc. 0.10–0.11
method	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
no draft ( $D0$ )	270.8 $\downarrow$ ( 1.00 $\uparrow$ )		269.2 $\downarrow$ ( 1.00 $\uparrow$ )		271.4 $\downarrow$ ( 1.00 $\uparrow$ )		271.8 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	79.1 ( 2.58 )	62.0 ( 2.57 )	57.5 ( 3.49 )	40.7 ( 3.26 )	67.1 ( 3.10 )	48.9 ( 3.16 )	88.9 ( 2.30 )	72.0 ( 2.29 )
SPOT- $\gamma$ (ours)	79.8 ( 2.60 )	66.2 ( 2.93 )	58.4 ( 3.56 )	43.4 ( 4.23 )	67.5 ( 3.28 )	51.7 ( 3.95 )	90.1 ( 2.40 )	76.7 ( 2.67 )
Spiffy graph	98.7 ( 2.31 )	82.3 ( 2.57 )	86.5 ( 2.78 )	66.6 ( 2.62 )	91.7 ( 2.70 )	72.4 ( 3.07 )	104.5 ( 2.40 )	90.0 ( 2.52 )

Appendix

Table 11: SDAR-1.7B b32 at

T{=}1

(coupled-noise match; free chain also under rejection sampling). Lowest NFE in every comparison and the higher throughput ratio in

28

32

; SPOT-

\gamma

wins every comparison on both columns. The ratio’s standard deviation over seeds is at most

0.12

NFE $\downarrow$ ( tok/s $\uparrow$ )	GSM8K		MBPP		HumanEval		MATH500
	acc. 0.59–0.65		acc. 0.28–0.35		acc. 0.66–0.68		acc. 0.10–0.12
method	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
no draft ( $D0$ )	271.6 $\downarrow$ ( 1.00 $\uparrow$ )		270.4 $\downarrow$ ( 1.00 $\uparrow$ )		269.3 $\downarrow$ ( 1.00 $\uparrow$ )		270.2 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	83.6 ( 2.32 )	64.0 ( 2.62 )	96.0 ( 2.04 )	75.6 ( 2.16 )	88.5 ( 2.86 )	65.8 ( 3.27 )	85.1 ( 2.33 )	66.5 ( 2.59 )
Spiffy graph	98.0 ( 1.59 )	80.8 ( 2.22 )	103.3 ( 2.01 )	86.6 ( 2.03 )	99.8 ( 2.69 )	78.7 ( 3.05 )	98.7 ( 2.11 )	80.6 ( 2.28 )
SSD free chain	95.9 ( 2.14 )	90.1 ( 2.08 )	103.0 ( 1.99 )	96.3 ( 1.91 )	100.5 ( 2.73 )	88.8 ( 2.77 )	97.7 ( 1.58 )	91.4 ( 1.59 )

Appendix

Table 12: Main results, LLaDA2.0-mini b32 (MoE, exact prefix-KV cache),

T{=}0

n{=}100

; MBPP and GSM8K with three seeds, MATH500 seed 0, HumanEval seed 0 except two

D8

baseline entries that are two-seed means. SPOT has the lowest NFE in all 36 comparisons and the higher throughput ratio in 34; the two exceptions are MBPP and HumanEval at

D12

, where Spiffy is ahead by

0.7\%

and

0.1\%

; mini’s per-round acceptance is low for every drafter (

1.05

–

3.77

accepted tokens per drafted round across the four tasks), so the wall-clock margins are thin on the code tasks.

	NFE $\downarrow$ ( tok/s $\uparrow$ )
drafter	$D8$	$D12$	$D20$
SPOT	102.3 ( 2.00 )	94.1 ( 2.04 )	82.1 ( 2.00 )
setting-specific drafter	108.5 ( 1.80 )	99.0 ( 1.87 )	85.1 ( 1.93 )

Appendix

Table 13: LLaDA2.0-mini b32 at

T{=}1

(MBPP,

n{=}100

, seed 0), the setting’s only

T{=}1

evidence: SPOT against a drafter tuned for this setting alone.

		NFE $\downarrow$ ( tok/s $\uparrow$ ) at $D8$
target	drafter	GSM8K	MBPP	HumanEval	MATH500
SDAR-8B	SDAR-8B ∗	69.6 ( 2.50 )	56.7 ( 2.61 )	62.2 ( 2.74 )	84.5 ( 2.03 )
	SDAR-4B	71.4 ( 2.37 )	57.6 ( 2.44 )	64.1 ( 2.75 )	85.9 ( 1.98 )
	SDAR-1.7B	72.0 ( 2.36 )	57.4 ( 2.46 )	65.3 ( 2.69 )	88.9 ( 1.86 )
	mini	72.8 ( 2.33 )	58.6 ( 2.34 )	66.8 ( 2.48 )	87.9 ( 1.91 )
SDAR-4B	SDAR-8B	69.3 ( 3.11 )	54.6 ( 3.42 )	63.3 ( 3.29 )	83.7 ( 2.60 )

Appendix

Table 14: Every checkpoint against every target it can drive,

T{=}0

, b32,

D8

, padded. ∗ marks the target’s native drafter, the one trained on it; all other rows are transferred with no retraining or recalibration. Ratio is against that target’s own draft-free control, best per column within a target in bold. The LLaDA2.0-mini rows are one seed. † no exact prefix cache, as in Table 3 .

	NFE $\downarrow$ ( tok/s $\uparrow$ )
setting	$D8$	$D12$	$D20$
SDAR-8B b32	55.6 ( 2.64 )	47.1 ( 2.42 )	38.7 ( 1.75 )
SDAR-8B b16	60.8 ( 3.46 )	58.7 ( 3.29 )	44.4 ( 3.23 )
mini b32	96.0 ( 2.04 )	86.9 ( 2.12 )	75.6 ( 2.16 )
mini b16	90.5 ( 1.98 )	82.1 ( 2.08 )	72.6 ( 2.19 )

Appendix

Table 15: Recipe transfer across widths and targets (MBPP,

T{=}0

n{=}100

): the single SPOT recipe vs. a drafter tuned separately for each setting.

	length 64		length 256		length 512
method	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
no draft ( $D0$ )	77.2 $\downarrow$ ( 1.00 $\uparrow$ )		269.2 $\downarrow$ ( 1.00 $\uparrow$ )		525.2 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	27.5 ( 1.56 )	22.2 ( 0.89 )	60.1 ( 2.45 )	42.6 ( 1.59 )	100.2 ( 2.79 )	66.7 ( 1.98 )
SPOT- $\gamma$ (ours)	31.8 ( 1.87 )	30.3 ( 1.87 )	64.9 ( 2.80 )	52.1 ( 2.86 )	105.1 ( 3.10 )	76.3 ( 3.23 )
Spiffy graph	30.9 ( 1.45 )	27.0 ( 0.76 )	86.3 ( 1.77 )	64.8 ( 1.07 )	158.4 ( 1.86 )	112.9 ( 1.21 )
free chain, match	31.0 ( 1.38 )	29.6 ( 0.65 )	87.4 ( 1.76 )	79.1 ( 0.88 )	159.5 ( 1.82 )	143.1 ( 0.92 )

Appendix

Table 16: Generation length, SDAR-8B b32 MBPP at

T{=}1

: NFE per sample ( throughput ratio over that length’s own draft-free control), best in bold. The

256

columns are the

T{=}1

MBPP block of Table 2 .

	NFE $\downarrow$ ( tok/s $\uparrow$ )
configuration	$D8$	$D20$
final recipe (tree, hedge $0.6$ , $\tau{=}1$ , $\gamma{=}0$ , padded)	56.7 ( 2.61 )	39.6 ( 1.72 )
$-$ token hedge (gate off)	57.0 ( 2.61 )	40.3 ( 1.68 )
chain instead of tree	64.0 ( 2.32 )	51.5 ( 1.34 )
$-$ scaled training corpus	57.3 ( 2.60 )	40.4 ( 1.72 )
no padding, $\gamma{=}0$	56.7 ( 2.59 )	39.6 ( 1.76 )

Appendix

Table 17: Ablations on SDAR-8B MBPP b32 at

T{=}0

(ratio standard deviation over seeds at most

0.11

). Top: recipe components. Bottom: padding and the mass floor

\gamma

, the two knobs that trade forwards for wall clock. The full

\gamma

grid and the

\tau

ablation are in the released records.

NFE $\downarrow$ ( tok/s $\uparrow$ )	GSM8K			MBPP
	acc. 0.89–0.90			acc. 0.41–0.43
method	$D8$	$D12$	$D20$	$D8$	$D12$	$D20$
no draft ( $D0$ )	270.8 $\downarrow$ ( 1.00 $\uparrow$ )			269.2 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	69.6 ( 2.50 )	60.9 ( 2.31 )	52.6 ( 1.56 )	56.7 ( 2.61 )	48.2 ( 2.38 )	39.6 ( 1.72 )
SPOT- $\gamma$ (ours)	75.1 ( 2.76 )	70.9 ( 2.83 )	67.8 ( 2.78 )	60.7 ( 2.98 )	54.1 ( 3.06 )	47.8 ( 2.99 )
Spiffy graph	91.3 ( 1.96 )	82.8 ( 1.71 )	71.9 ( 1.14 )	83.4 ( 1.86 )	74.9 ( 1.59 )	61.3 ( 1.17 )

Appendix

Table 18: SDAR-8B b32,

T{=}0

, all three budgets: GSM8K and MBPP. NFE is identical across seeds at

T{=}0

; the throughput ratio has standard deviation at most

0.11

, median

0.04

NFE $\downarrow$ ( tok/s $\uparrow$ )	HumanEval			MATH500
	acc. 0.74–0.74			acc. 0.10–0.11
method	$D8$	$D12$	$D20$	$D8$	$D12$	$D20$
no draft ( $D0$ )	271.4 $\downarrow$ ( 1.00 $\uparrow$ )			271.8 $\downarrow$ ( 1.00 $\uparrow$ )
SPOT (ours)	62.2 ( 2.74 )	53.3 ( 2.67 )	44.6 ( 1.85 )	84.5 ( 2.03 )	75.1 ( 1.80 )	66.0 ( 1.20 )
SPOT- $\gamma$ (ours)	66.5 ( 3.09 )	61.0 ( 3.19 )	56.4 ( 3.13 )	92.2 ( 2.27 )	89.9 ( 2.27 )	89.5 ( 2.27 )
Spiffy graph	86.8 ( 2.11 )	78.2 ( 1.87 )	65.9 ( 1.28 )	99.4 ( 1.80 )	90.5 ( 1.58 )	82.7 ( 0.99 )

Appendix

Table 19: SDAR-8B b32,

T{=}0

, all three budgets: HumanEval and MATH500. Seed spread as in Table 18 .

		$D0$	$D3$	$D5$	$D6$	$D8$	$D12$	$D16$	$D20$
SPOT, GSM8K	NFE $\downarrow$	271.1	102.4	84.2	78.0	69.5	60.8	54.7	52.6
SPOT, GSM8K	tok/s $\uparrow$	1.00	2.38	2.69	2.80	2.60	2.43	1.85	1.63
SPOT, MBPP	NFE $\downarrow$	267.1	87.7	70.9	63.9	55.6	47.1	39.7	38.7
SPOT, MBPP	tok/s $\uparrow$	1.00	2.25	2.80	3.04	2.70	2.47	2.15	1.79
SPOT, HumanEval	NFE $\downarrow$	272.6	96.5	78.0	71.1	62.2	53.4	46.7	44.4
SPOT, HumanEval	tok/s $\uparrow$	1.00	2.51	2.88	3.13	2.82	2.68	2.27	1.87

Appendix

Table 20: Budget response,

T{=}0

n{=}100

(three seeds at every budget shown on the SDAR-8B settings; mini seed 0 except

D0/6/8/12/20

). Bold: throughput optimum.

Figure 3: Budget curves (SDAR-8B,

n{=}100

T{=}0

). Left: NFE vs. draft budget for SPOT (solid) and, on MBPP, the fixed baselines at

D8/12/20

(markers). Right: throughput ratio over the shared draft-free control for SPOT, non-monotone with an interior optimum at

D6

on every task.

		coupled-noise match		uncoupled match		greedy match †
$T$	drafter	$D8$	$D20$	$D8$	$D20$	$D8$	$D20$
0.5	no draft ( $D0$ )	267.1 NFE, accuracy 0.35, argmax fraction 0.988, mean committed $p$ 0.993
	SPOT	56.8 (2.56)	39.2 (1.74)	56.7 (2.53)	39.1 (1.68)	55.9 (2.62)	38.9 (1.76)
	Spiffy graph	83.0 (1.83)	60.4 (1.16)	82.7 (1.87)	60.3 (1.19)	82.3 (1.83)	59.9 (1.16)
	BlockSpec-style tree	135.6 (1.12)	112.0 (0.60)	135.1 (1.10)	111.4 (0.59)	134.8 (1.12)	111.3 (0.60)
1.0	no draft ( $D0$ )	267.1 NFE, accuracy 0.38, argmax fraction 0.978, mean committed $p$ 0.967

Appendix

Table 21: Complete temperature sweep, SDAR-8B MBPP b32,

n{=}100

, seed 0: NFE (tok/s ratio over the

T

-matched draft-free control) for every drafter under the three equality verifiers at

D8

and

D20

. † greedy match is not distribution-preserving at

T>0

(Proposition 2 does not apply); its NFE is not comparable to the exact regimes’ and its emitted text drifts from the target’s distribution (Table 1 ).

		NFE $\downarrow$ ( tok/s $\uparrow$ )
drafter	verifier	$D8$	$D12$	$D20$
SPOT	tree + match	60.1 ( 2.45 )	51.5 ( 2.18 )	42.6 ( 1.59 )
SPOT	chain + match	71.6 ( 2.01 )	65.6 ( 1.70 )	59.3 ( 1.12 )
SPOT	chain + RS	68.7 ( 1.91 )	62.7 ( 1.64 )	56.3 ( 1.12 )

Appendix

Table 22: Verifier and structure at

T{=}1

, SDAR-8B MBPP: SPOT’s proposals under each verifier (match: coupled-noise match; RS: rejection sampling, chains only). Over seeds the ratio’s standard deviation is at most

0.09

Figure 4: Left: stale-order knowledge decays across blocks (previous round’s top-confidence position still commits) while the stale argmax token stays right. Right: accepted tokens per drafted round by block,

D20

, SDAR-8B MBPP.

Figure 5: Left: acceptance calibration of the drafter’s own node score (realized

P(\text{accept})

per prefix-mass bin against the diagonal). Right: first-rejection attribution by block (

D20

): position misses dominate early, deep blocks are budget-bound. Development runs of the final drafter.

Speculative Decoding for Diffusion Language Models

Speculative decoding for diffusion language models speeds generation by drafting tokens in parallel and verifying them efficiently.

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Aug 27, 2026J/K move · Enter open · S save

Trajectory-Level Speculative Decoding for Diffusion Language Models

Tianxiang Pan, Baitao Gong, Mo Guang, Hongwei Yong+4

Li Auto Inc., Shanghai, China

Speculative Decoding for Diffusion Language Models Diffusion Language Model Decoding Speculative Decoding Diffusion Language Model Inference

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Diffusion-based language models (dLLMs) enable parallel token generation through iterative denoising, but existing decoding strategies collapse to single-token generation under low confidence, severely limiting throughput. Unlike autoregressive models where speculative decoding operates on token sequences in a fixed left-to-right order, dLLMs require speculating over denoising trajectories-sequences of multi-token updates with explicit positions and unmasking orders. We develop a trajectory-level speculative framework that constructs draft denoising trajectories via confidence-stratified tree exploration and verifies them through blockwise parallel evaluation with bidirectional attention masking. Our method further introduces inter-block speculation, exploiting diffusion models' bidirectional structure to perform cross-block lookahead. We formally characterize when this approach is exact and identify trajectory drift as the fundamental cost of increased parallelism. Building on Fast-dLLM's dual-cache infrastructure, our framework reduces denoising iterations by 30-40% and increases tokens-per-step from 2.6 to 4.3, achieving 7-14x speedup over vanilla dLLMs and 1.3x over Fast-dLLM with less than 1% accuracy change across reasoning and code benchmarks.

Abstract

Speculative Decoding for Diffusion Language Models

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