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
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× (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 at T=0.5 to 8.5 at T=2.5 . † Greedy match is not distribution-preserving, so its NFE is not comparable.
NFE ↓ ( tok/s ↑ )
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 ↓ ( 1.00 ↑ )
269.2 ↓ ( 1.00 ↑ )
271.4 ↓ ( 1.00 ↑ )
271.8 ↓ ( 1.00 ↑ )
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- γ (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- γ : unpadded, γ=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 ↓ at D8
GSM8K
MBPP
HumanEval
MATH500
target \ 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
γ=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×
1.23×
1.23×
1.17×
SPOT (ours)
2.79× (3.6)
2.49× (3.2)
3.15× (4.2)
3.61× (4.9)
SDAR-4B
MRP (reported)
1.36×
1.26×
1.35×
1.27×
SPOT (ours)
3.17× (4.0)
2.63× (3.3)
3.48× (4.4)
3.48× (4.9)
SDAR-8B
MRP (reported)
1.40×
1.39×
1.34×
1.34×
SPOT (ours)
2.50× (3.9)
2.03× (3.2)
2.74× (4.4)
2.61× (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 × )
43.0 (6.3 × )
38.2 (7.1 × )
68.6 (3.9 × )
64.8 (4.2 × )
62.1 (4.4 × )
46.8 (5.8 × )
38.2 (7.1 × )
31.3 (8.7 × )
tok/s ratio
18.4 tok/s
3.89 ×
4.02 ×
3.25 ×
2.81 ×
2.60 ×
1.89 ×
4.19 ×
4.56 ×
4.02 ×
SDAR-8B b32 MBPP
NFE
267.1
46.8 (5.7 × )
39.7 (6.7 × )
33.0 (8.1 × )
53.7 (5.0 × )
47.2 (5.7 × )
40.9 (6.5 × )
43.7 (6.1 × )
35.4 (7.5 × )
27.5 (9.7 × )
tok/s ratio
18.7 tok/s
3.25 ×
3.36 ×
3.05 ×
2.82 ×
2.77 ×
2.35 ×
3.50 ×
3.77 ×
3.53 ×
SDAR-8B b32 HumanEval
NFE
272.6
47.5 (5.7 × )
40.0 (6.8 × )
33.4 (8.2 × )
62.3 (4.4 × )
57.6 (4.7 × )
53.6 (5.1 × )
46.1 (5.9 × )
37.9 (7.2 × )
30.3 (9.0 × )
Appendix
Table 7: Live-oracle grid, T=0 , generation length 256, n=100 , seed 0. Per setting: NFE (reduction × 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 ↓ ( tok/s ↑ )
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 ↓ ( 1.00 ↑ )
269.2 ↓ ( 1.00 ↑ )
271.4 ↓ ( 1.00 ↑ )
271.8 ↓ ( 1.00 ↑ )
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- γ (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 ↓ ( tok/s ↑ )
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 ↓ ( 1.00 ↑ )
269.2 ↓ ( 1.00 ↑ )
271.4 ↓ ( 1.00 ↑ )
271.8 ↓ ( 1.00 ↑ )
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- γ (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 ↓ ( tok/s ↑ )
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 ↓ ( 1.00 ↑ )
269.2 ↓ ( 1.00 ↑ )
271.4 ↓ ( 1.00 ↑ )
271.8 ↓ ( 1.00 ↑ )
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- γ (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 of 24 ; SPOT- γ , which drops the padding, leads in 23 . The ratio’s standard deviation over seeds is at most 0.17 .
NFE ↓ ( tok/s ↑ )
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 ↓ ( 1.00 ↑ )
269.2 ↓ ( 1.00 ↑ )
271.4 ↓ ( 1.00 ↑ )
271.8 ↓ ( 1.00 ↑ )
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- γ (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 of 32 ; SPOT- γ wins every comparison on both columns. The ratio’s standard deviation over seeds is at most 0.12 .
NFE ↓ ( tok/s ↑ )
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 ↓ ( 1.00 ↑ )
270.4 ↓ ( 1.00 ↑ )
269.3 ↓ ( 1.00 ↑ )
270.2 ↓ ( 1.00 ↑ )
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 ↓ ( tok/s ↑ )
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 ↓ ( tok/s ↑ ) 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 ↓ ( tok/s ↑ )
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 ↓ ( 1.00 ↑ )
269.2 ↓ ( 1.00 ↑ )
525.2 ↓ ( 1.00 ↑ )
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- γ (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 .
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 γ , the two knobs that trade forwards for wall clock. The full γ grid and the τ ablation are in the released records.
NFE ↓ ( tok/s ↑ )
GSM8K
MBPP
acc. 0.89–0.90
acc. 0.41–0.43
method
D8
D12
D20
D8
D12
D20
no draft ( D0 )
270.8 ↓ ( 1.00 ↑ )
269.2 ↓ ( 1.00 ↑ )
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- γ (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 ↓ ( tok/s ↑ )
HumanEval
MATH500
acc. 0.74–0.74
acc. 0.10–0.11
method
D8
D12
D20
D8
D12
D20
no draft ( D0 )
271.4 ↓ ( 1.00 ↑ )
271.8 ↓ ( 1.00 ↑ )
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- γ (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 ↓
271.1
102.4
84.2
78.0
69.5
60.8
54.7
52.6
tok/s ↑
1.00
2.38
2.69
2.80
2.60
2.43
1.85
1.63
SPOT, MBPP
NFE ↓
267.1
87.7
70.9
63.9
55.6
47.1
39.7
38.7
tok/s ↑
1.00
2.25
2.80
3.04
2.70
2.47
2.15
1.79
SPOT, HumanEval
NFE ↓
272.6
96.5
78.0
71.1
62.2
53.4
46.7
44.4
tok/s ↑
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 ↓ ( tok/s ↑ )
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(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.
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.
Diffusion large language models (dLLMs) have recently emerged as a promising alternative to autoregressive (AR) LLMs, offering faster inference through parallel or blockwise decoding. However, their masked language modeling formulation remains incompatible with standard token-level speculative decoding, one of the most effective acceleration techniques for AR models. In AR decoding, the causal mask preserves temporally valid token-level contexts, enabling a target model to verify multiple drafted tokens in a single forward pass. In contrast, dLLMs rely on mask tokens and bidirectional attention, causing the effective context to change across denoising steps and preventing direct token-level speculative verification. To bridge this gap, we propose a simple but effective speculative decoding algorithm for diffusion language models, named SimSD, which mainly adopts a plug-and-play masking strategy that equips dLLMs with temporally valid token-level contexts for speculative decoding. Our method explicitly introduces reference tokens from draft-model predictions and designs an attention mask that regulates their interaction with current-step tokens, allowing dLLMs to compute valid logits for drafted tokens in a single forward pass. This restores the key verification ability provided by causal masking in AR models while preserving the parallel decoding advantages of dLLMs. The proposed method is training-free and can be flexibly integrated with other acceleration techniques such as KV cache and blockwise decoding. Experiments on SDAR-family dLLMs across four benchmarks show that our method achieves up to 7.46x higher decoding throughput while maintaining and even improving average generation quality.
Junxia Cui, Haotian Ye, Runchu Tian +9
University of California San Diego · University of Illinois Urbana-Champaign · 3Google +1
Large language models (LLMs) achieve remarkable performance across a wide range of tasks, but their autoregressive decoding process incurs substantial inference costs due to inherently sequential token generation. Speculative decoding addresses this bottleneck by employing a lightweight draft model to propose multiple future tokens that are subsequently verified in parallel by a larger target model. Recent work has demonstrated that diffusion language models are well suited for this setting, as they can generate entire blocks of draft tokens in parallel and thereby alleviate the sequential constraints of autoregressive drafting. A subtlety of this regime is that block-diffusion drafters generate tokens bidirectionally within a block, whereas verification is performed by an autoregressive target model that evaluates tokens in a strictly left-to-right manner, leaving a gap between the symmetric training-time objective and the asymmetric verification-time reward. In this work, we offer an empirical analysis of three training-time interventions that narrow this gap: token positional weighting, a first-error focal loss that targets the position that breaks the accepted prefix within each block, and a chain loss term that substitutes a differentiable surrogate for the expected accepted length. The three interventions act along orthogonal axes (position, block-conditional first error, joint prefix) and compose additively; they are likewise orthogonal to test-time alignment mechanisms such as multi-draft self-selection, with which they can in principle be combined. Across four target models and six reasoning, code, and dialogue benchmarks, the three interventions raise accepted draft length by 21-76% per benchmark over a position-uniform baseline, without adding additional forward passes and without changing the inference pipeline or the rejection-sampling exactness contract.