Faster Block-Diffusion Serving with Distribution-Free Risk Guarantees

Jungseob Lee; Dongyub Jude Lee; Chanjun Park; Sugyeong Eo; Heuiseok Lim

cs.CLSep 27, 2026

Faster Block-Diffusion Serving with Distribution-Free Risk Guarantees

Authors: Jungseob Lee, Dongyub Jude Lee, Chanjun Park, Sugyeong Eo, Heuiseok Lim

Organizations: Korea University · Zoom Communications · Soongsil University · Yonsei University Mirae Campus

Abstract

Block-diffusion language models are served at hand-picked operating points, such as acceptance thresholds, buffer depth, schedule, checkpoint and precision, and each point is chosen by its mean benchmark accuracy. However, a mean does not tell an operator how often a faster configuration fails on prompts that the slower one answers correctly. On the serving engine and its decode traces, the default commit rule already commits every fully resolved block, a static skip rule captures nearly all of the compute that allocation can save, and self-distillation on engine-decoded targets adds speed at unchanged accuracy. Larger speedups come from lower thresholds, which commit tokens that are still uncertain. We therefore present Redline, a finite-sample procedure that selects operating points, hand-picked or learned, from the correctness of their answers on calibration prompts. Redline keeps the reference-relative risk, the joint probability that the reference answers correctly and a candidate configuration does not, within a user-chosen budget with high probability, and deploys the fastest configuration that passes. It speeds up math at a smaller risk budget than code in both model families, and at a budget of ten percent it deploys a LLaDA2 math configuration that commits over a third more tokens in each forward. It also applies without modification to the acceptance rule of speculative decoding and to weight quantization. On the same calibration data, Redline stays within its stated failure probability, whereas each tolerance of a mean-accuracy rule either gains less speed for some model and task or exceeds the risk budget far more often for another. Code is available at https://github.com/js-lee-AI/Redline.

Figures & tables

	engine accuracy			engine TPF
$\tau_{\text{add}}$	0.05	0.10	0.20	0.05	0.10	0.20
base	0.895	0.895	0.902	3.20	3.18	3.19
distilled	0.898	0.902	0.902	3.36	3.37	3.37
change	$+0.39$	$+0.78$	$+0.00$	$+5.2$	$+5.8$	$+5.8$

Table 1: Self-distillation on engine-decoded targets, SDAR on

256

held-out GSM8K prompts. Engine accuracy and TPF at each admission threshold

\tau_{\text{add}}

, with the change in points and in percent.

				$\alpha=0.10$		$\alpha=0.15$		$\alpha=0.20$
grid	$n$	$m$	$\alpha_{\min}$	gain	$\Delta$ acc.	gain	$\Delta$ acc.	gain	$\Delta$ acc.
[0pt][0pt] Block-diffusion serving, TPF gain (%)
LLaDA2 math	$1{,}012$	$7$	$0.07$	$+37.5$	$-4.0$	$+37.5$	$-4.0$	$+37.5$	$-4.0$
LLaDA2 math, large grid	$1{,}012$	$50$	$0.07$	$+65.4$	$-3.4$	$+72.0$	$-5.9$	$+72.0$	$-5.9$
LLaDA2 code	$542$	$8$	$0.11$	$0.0$	$0.0$	$+33.7$	$-7.0$	$+42.4$	$-13.1$
SDAR math	$1{,}012$	$8$	$0.10$	$+13.1$	$-2.5$	$+36.6$	$-4.6$	$+36.6$	$-4.6$

Table 2: Configurations that Redline deploys at three risk budgets (

\delta=0.10

, Holm), with the gain over the reference in the group’s cost measure and the net accuracy change in points. Below

\alpha_{\min}

, the smallest budget at which a cheaper configuration passes, the reference is deployed.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

$\lambda$ , $\Lambda$	a serving configuration and the finite grid of configurations searched, spanning accept and semi-completion thresholds, block-add schedule, buffer depth, checkpoint and precision
reference	the conservative baseline configuration of each grid, which is the engine’s default for block diffusion, lossless verification for speculative decoding and bf16 weights for quantization
$R(\lambda)$	reference-relative risk, the joint probability that the reference answers a prompt correctly and $\lambda$ does not. It upper-bounds the net accuracy drop
$\alpha$	the risk budget. The guarantee asserts $R(\lambda)\leq\alpha$
$\delta$	the failure probability. All statements about one grid hold jointly with probability at least $1-\delta$ , and $\delta=0.10$ throughout
TPF	tokens committed in each model forward, a count ratio independent of host speed. The speculative-decoding analogue is the number of accepted tokens for each target forward
$n$	the number of calibration prompts of a grid

Appendix

Table 3: Notation used throughout the paper.

					$p$ -value at budget $\alpha$
configuration	TPF	forwards	tokens	$\hat{R}$ ( $k/n$ )	$0.05$	$0.10$	$0.15$	$0.20$
[0pt][0pt] Hand-picked configurations of the SDAR math grid
acc85/semi70	5.829	147.2	858	0.106 (53/500)	1.000	0.704	0.003	1e-8
acc90/semi70	5.490	164.5	903	0.118 (59/500)	1.000	0.919	0.023	8e-7
acc85/semi90	5.390	161.2	869	0.102 (51/500)	1.000	0.596	0.001	3e-9
acc90/semi90	4.752	177.9	845	0.094 (47/500)	1.000	0.361	1e-4	9e-11

Appendix

Table 4: Redline on MATH-500 (

n=500

) over the eight hand-picked SDAR math configurations and the distilled checkpoint at the same threshold settings (

m=16

). TPF, forwards and tokens of each request, joint risk

\hat{R}

and

p

-values. Bold marks configurations valid under Holm, and underlining the deployed one.

		gain		net accuracy		joint risk
grid	$\alpha$	value	$95\%$ interval	value	$95\%$ interval	$\hat{R}$	$95\%$ interval	$90\%$ bound
[0pt][0pt] Block-diffusion serving, TPF gain (%)
LLaDA2 math	$\geq 0.10$	$+37.5$	$[34.0,41.1]$	$-4.0$	$[-5.9,-2.0]$	$0.072$	$[0.057,0.090]$	$0.084$
LLaDA2 math, large grid	$0.10$	$+65.4$	$[60.8,70.2]$	$-3.4$	$[-5.4,-1.4]$	$0.073$	$[0.058,0.091]$	$0.085$
LLaDA2 math, large grid	$\geq 0.15$	$+72.0$	$[67.7,76.3]$	$-5.9$	$[-8.2,-3.8]$	$0.098$	$[0.080,0.118]$	$0.111$
LLaDA2 code	$0.15$	$+33.7$	$[26.8,41.1]$	$-7.0$	$[-10.1,-3.9]$	$0.109$	$[0.084,0.138]$	$0.128$

Appendix

Table 5: Intervals for every configuration that Redline deploys, other than the reference. Gain and net accuracy change with

95\%

paired-bootstrap intervals over prompts, and joint risk

\hat{R}

with its

95\%

Clopper–Pearson interval and one-sided

90\%

upper bound. Budgets that deploy the same configuration share a row.

family	draw	$n$	median	IQR	$\leq 0.10$	$<0.11$	$\leq 0.11$	draws by smallest budget with a gain, $0.05$ to $0.12$
LLaDA2 math	uniform	542	0.08	[0.07, 0.08]	1.000	1.000	1.000	0, 52, 334, 543, 70, 1, 0, 0
LLaDA2 math	stratified	542	0.08	[0.07, 0.08]	1.000	1.000	1.000	1, 36, 324, 551, 87, 1, 0, 0
SDAR math	uniform	664	0.10	[0.10, 0.11]	0.739	0.739	0.991	0, 0, 0, 14, 224, 501, 252, 9
SDAR math	stratified	664	0.10	[0.09, 0.11]	0.741	0.741	0.994	0, 0, 0, 13, 252, 476, 253, 6

Appendix

Table 6: Smallest math budget with a gain, with the math set subsampled to the code

n

, over

1{,}000

uniform or benchmark-stratified draws for each family (Redline,

\delta=0.10

, fine budget grid). Median, interquartile range, shares of draws under the listed budgets, and the draws at each budget.

configuration	TPF	forwards	tokens	$\hat{R}$ ( $k/n$ )	$0.05$	$0.10$	$0.15$	$0.20$
					$p$ -value at budget $\alpha$
acc85/semi70	6.050	128.8	779	0.072 (73/1012)	0.999	0.001	3e-14	5e-30
acc85/semi90	5.850	134.3	786	0.066 (67/1012)	0.990	1e-4	1e-16	4e-33
acc90/semi70	5.456	144.4	788	0.064 (65/1012)	0.981	4e-5	2e-17	3e-34
acc90/semi90	5.165	149.5	772	0.053 (54/1012)	0.718	6e-8	2e-22	7e-41
acc95/semi70	4.571	171.4	784	0.051 (52/1012)	0.616	1e-8	2e-23	3e-42

Appendix

Table 8: Full grid for LLaDA2 math. TPF, forwards and tokens of each request, joint risk

\hat{R}

(

k/n

) and exact binomial

p

-values at four budgets. Bold marks the configurations valid under Holm, and underlining the one Redline deploys.

configuration	TPF	forwards	tokens	$\hat{R}$ ( $k/n$ )	$0.05$	$0.10$	$0.15$	$0.20$
					$p$ -value at budget $\alpha$
acc85/semi70	7.566	28.9	219	0.157 (85/542)	1.000	1.000	0.697	0.006
acc85/semi90	7.107	28.6	203	0.109 (59/542)	1.000	0.778	0.003	9e-9
acc90/semi70	6.793	30.4	207	0.138 (75/542)	1.000	0.998	0.245	1e-4
acc90/semi90	6.206	34.0	211	0.076 (41/542)	0.996	0.031	1e-7	7e-16
acc95/semi70	5.495	38.3	210	0.100 (54/542)	1.000	0.525	4e-4	2e-10

Appendix

Table 9: Full grid for LLaDA2 code. TPF, forwards and tokens of each request, joint risk

\hat{R}

(

k/n

) and exact binomial

p

-values at four budgets. Bold marks the configurations valid under Holm, and underlining the one Redline deploys.

configuration	TPF	forwards	tokens	$\hat{R}$ ( $k/n$ )	$0.05$	$0.10$	$0.15$	$0.20$
					$p$ -value at budget $\alpha$
acc85/semi70	5.263	102.9	542	0.105 (106/1012)	1.000	0.714	2e-5	2e-16
acc90/semi70	4.956	115.0	570	0.099 (100/1012)	1.000	0.476	1e-6	2e-18
acc85/semi90	4.920	112.0	551	0.093 (94/1012)	1.000	0.244	4e-8	1e-20
acc90/semi90	4.361	123.9	540	0.071 (72/1012)	0.999	9e-4	1e-14	2e-30
acc95/semi70	4.296	136.0	584	0.083 (84/1012)	1.000	0.037	9e-11	8e-25

Appendix

Table 10: Full grid for SDAR math. TPF, forwards and tokens of each request, joint risk

\hat{R}

(

k/n

) and exact binomial

p

-values at four budgets. Bold marks the configurations valid under Holm, and underlining the one Redline deploys.

configuration	TPF	forwards	tokens	$\hat{R}$ ( $k/n$ )	$0.05$	$0.10$	$0.15$	$0.20$
					$p$ -value at budget $\alpha$
acc85/semi70	4.253	17.2	73	0.178 (118/664)	1.000	1.000	0.978	0.081
acc85/semi90	3.810	18.0	69	0.145 (96/664)	1.000	1.000	0.372	1e-4
acc90/semi70	3.492	19.4	68	0.139 (92/664)	1.000	0.999	0.222	2e-5
acc90/semi90	3.349	20.6	69	0.087 (58/664)	1.000	0.153	9e-7	1e-15
acc95/semi70	2.980	23.7	71	0.081 (54/664)	1.000	0.059	7e-8	3e-17

Appendix

Table 11: Full grid for SDAR code. TPF, forwards and tokens of each request, joint risk

\hat{R}

(

k/n

) and exact binomial

p

-values at four budgets. Bold marks the configurations valid under Holm, and underlining the one Redline deploys.

configuration	TPF	forwards	tokens	$\hat{R}$ ( $k/n$ )	$0.05$	$0.10$	$0.15$	$0.20$
					$p$ -value at budget $\alpha$
acc85/semi70	5.973	131.7	787	0.057 (29/512)	0.789	3e-4	3e-11	2e-20
acc85/semi90	5.850	129.8	759	0.070 (36/512)	0.983	0.012	2e-8	2e-16
acc90/semi70	5.317	146.2	778	0.064 (33/512)	0.941	0.003	2e-9	5e-18
acc90/semi90	5.245	150.9	792	0.053 (27/512)	0.659	8e-5	3e-12	1e-21
acc95/semi70	4.534	165.4	750	0.051 (26/512)	0.584	4e-5	1e-12	2e-22

Appendix

Table 12: Full grid for LLaDA2 math on the reduced prompt set. TPF, forwards and tokens of each request, joint risk

\hat{R}

(

k/n

) and exact binomial

p

-values at four budgets. Bold marks the configurations valid under Holm, and underlining the one Redline deploys.

configuration	TPF	forwards	tokens	$\hat{R}$ ( $k/n$ )	$0.05$	$0.10$	$0.15$	$0.20$
					$p$ -value at budget $\alpha$
acc85/semi70	7.619	28.6	218	0.143 (60/420)	1.000	0.998	0.372	0.001
acc85/semi90	7.224	31.8	230	0.121 (51/420)	1.000	0.936	0.055	1e-5
acc90/semi70	6.536	32.7	214	0.117 (49/420)	1.000	0.887	0.030	4e-6
acc90/semi90	6.339	34.2	217	0.090 (38/420)	1.000	0.290	2e-4	7e-10
acc95/semi70	5.492	40.1	220	0.093 (39/420)	1.000	0.349	3e-4	2e-9

Appendix

Table 13: Full grid for LLaDA2 code on the reduced prompt set. TPF, forwards and tokens of each request, joint risk

\hat{R}

(

k/n

) and exact binomial

p

-values at four budgets. Bold marks the configurations valid under Holm, and underlining the one Redline deploys.

	Redline			MEAN ( $t$ ) just slower			MEAN ( $t$ ) at or faster			MEAN ( $10$ )
$\alpha$	gain	exc.	ref.	$t$	gain	exc.	$t$	gain	exc.	gain	exc.
LLaDA2 math
0.05	0.0	0.1	99.9	none slower			0	0.6	5.7	37.5	99.6
0.10	36.6	0.1	0.0	5	36.6	0.1	6	37.3	0.1	37.5	0.1
0.15	37.5	0.0	0.0	6	37.3	0.0	7	37.5	0.0	37.5	0.0
0.20	37.5	0.0	0.0	6	37.3	0.0	7	37.5	0.0	37.5	0.0

Appendix

Table 14: Redline against the mean-accuracy rule MEAN(

t

) on

1{,}000

random half splits. Mean TPF gain, exceedance (splits with test-half

R>\alpha

) and deployments of the reference (ref.), all in percent, for the tolerances that bracket the gain of Redline and for

t=10

[0pt][0pt] LLaDA2 math ( $n=1{,}012$ )
							NETHOLM				MEAN ( $t$ )
$\alpha$	measure	Redline	BONF	FIXSEQ	UNCORR	PLUGIN	H	HB	WSR	MEANCI	slower	faster	$t=10$
0.05	gain	0.0	0.0	0.1	0.2	7.8	0.0	0.0	8.6	27.0	none	0.6	37.5
	test	0.1	0.1	1.6	2.4	58.4	0.0	0.0	47.9	89.6		5.7	99.6
	pool	0.1	0.1	1.6	2.4	58.4	0.0	0.0	50.3	99.5		5.7	100.0
0.10	gain	36.6	32.7	36.7	37.0	37.5	0.0	0.0	37.5	37.5	36.6	37.3	37.5

Appendix

Table 15: Every selector on the same

1{,}000

random half splits (

\delta=0.10

). Mean TPF gain of the deployed configuration, and exceedance on the test half and against the pooled risk, in percent.

		in sample		splits		held out
$\alpha$	deployed	gain	net	ref.	same	gain	net
LLaDA2 math
0.05	reference	+0.0	0.0	999	999	+0.0	0.0
0.10	acc85/semi70	+37.5	$-$ 4.0	0	894	+37.6 [+34.1, +41.3]	$-$ 4.2 [ $-$ 5.9, $-$ 2.6]
0.15	acc85/semi70	+37.5	$-$ 4.0	0	1000	+37.6 [+34.1, +41.4]	$-$ 4.0 [ $-$ 5.9, $-$ 2.2]
0.20	acc85/semi70	+37.5	$-$ 4.0	0	1000	+37.6 [+34.1, +41.4]	$-$ 4.0 [ $-$ 5.9, $-$ 2.2]

Appendix

Table 16: Held-out re-measurement over

1{,}000

random half splits of the configuration that Redline deploys on one half, measured on the other. Splits deploying the reference and the full-sample configuration, and held-out mean with

95\%

percentile range, gain in percent and net accuracy in points.

$\alpha$	deployed	valid	$k$	$\hat{R}$	TPF	TPF gain (%)	net accuracy (pp)
[0pt][0pt] The six configurations shared with the main grid, $m=6$
0.05	reference	1 of 6	0	0.000	4.42	$+0.0$	$+0.0$
0.10	acc85/semi70/add0.10	6 of 6	53	0.052	5.90	$+33.4$	$-1.5$
0.15	acc85/semi70/add0.10	6 of 6	53	0.052	5.90	$+33.4$	$-1.5$
0.20	acc85/semi70/add0.10	6 of 6	53	0.052	5.90	$+33.4$	$-1.5$
[0pt][0pt] The add $0.10$ slice, $m=25$

Appendix

Table 17: The LLaDA2 math grid of

50

configurations tested by Redline as three nested grids of the same served outputs (

n=1{,}012

\delta=0.10

). For each grid and budget, the deployed configuration, the number of valid configurations, its violations

k

, joint risk, TPF, gain and net accuracy change.

line of work	guarantee	multiplicity	mechanism	generality
BD-LM families and serving engine (BD3-LM, SDAR, LLaDA2.0 and 2.1, MBD-LM)	✗mean accuracy	✗hand-picked points	stall documented, unexplained	✗
learned-frontier line (distillation, multi-block visibility, RL shaping, in-place revision, Fast-dLLM and v2, D2F, AdaBlock, dParallel, LoPA, d3LLM, DMax)	✗	✗	✗	one cost each
Fast-dLLM Theorem 1	deterministic, conditional on trusting model confidence, no $\delta$	✗	✗	one threshold
CALM (LTT on AR early exit)	✓finite-sample, relative to the full model	one threshold	✗	early exit only
LTT and conformal risk control (frameworks)	✓	✓procedure	not a serving system
lossy AR acceleration (speculative decoding, Medusa typical acceptance, PTQ)	✗supply the settings	✗	✗	one cost each

Appendix

Table 18: Positioning against related work. Guarantee is a distribution-free finite-sample statement about deployed quality, multiplicity is error control over a space of configurations, mechanism is causal evidence for the operating point, and generality is one procedure across cost measures.

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