Machine translation tests masked diffusion language models (dLLMs) because every source token must be rendered faithfully, while fixed canvas decoding must choose target length before denoising. Existing masked diffusion decoding work mainly studies token unmasking order, leaving this length decision under-explored despite its direct effect on coverage and redundancy. We introduce Entropy-Valley (EV), a training-free length selector that scores candidate target canvases by mean predictive entropy from all-mask forward passes and selects the canvas the backbone is most prepared to fill. Relative to a baseline using training corpus length statistics, EV recovers 64.9%, 65.3%, and 33.0% of the COMET-22 gain from reference target lengths on En→Zh, Zh→En, and En→De. Our diagnostics show that denoising-friendly lengths need not match reference lengths. Evaluation by three translation experts supports the En↔Zh adequacy gains, with stronger evidence on Zh→En. Compared with a LLaMA-3-8B autoregressive (AR) model trained on the same fine-tuning data, the EV system ties on En→Zh and leads on Zh→En; an oracle-length diagnostic further shows that, in this masked diffusion MT setting, deciding which tokens to reveal first matters less than how the target length is supplied.
Figures & tables
Figure 1: Three En → Zh cases decoded with 32 denoising steps. A short canvas can drop an action verb or a required placeholder; EV chooses a longer canvas in these two cases and recovers the missing content. The third case shows the opposite boundary: the best compression lies below the EV candidate range, so the ratio baseline is better.
Figure 2: Entropy-Valley method overview. Given a source sentence, EV uses five candidate ratios from the fixed set R , yielding up to five distinct target canvases after duplicate lengths are removed. It then probes each candidate length once with an all-mask forward pass through the frozen LoRA-SFT LLaDA-8B model and records the mean predictive entropy Hˉ(L) over all slots except the designated EOS slot. EV selects the entropy valley, L⋆=argminLHˉ(L) , and decodes only this selected canvas with minimum-entropy decoding (MED) for T=32 steps. The procedure adds no parameters, does not use the reference length of the current sentence, and requires no length predictor.
Figure 3: Length-adaptive decoding for masked-diffusion MT. (A) Mean COMET-22 over three runs for a reference-length upper bound, EV, and a corpus-ratio baseline across three directions. EV closes 64.9% on En → Zh , 65.3% on Zh → En , and 33.0% on En → De . (B) Matched-data AR calibration across three directions. (C) Controlled En → Zh diagnostic: with reference target lengths fixed, the tested source-guided unmasking schedules span 0.0081 COMET. With the schedule fixed to MED, three length choices span 0.0265 COMET. The order-schedule sweep uses reference lengths, so it is a diagnostic rather than a deployable alternative to EV.
COMET-22
sacreBLEU
Direction
Method
Mean ± Std
Gap Closure
Mean ± Std
Gap Closure
En → Zh
Oracle length
0.8610±0.0013
100%
40.81±0.23
100%
Fixed ratio 0.8
0.8345±0.0017
0% (baseline)
36.72±0.22
0%
Entropy-Valley
0.8517±0.0006
64.9±7.4%
38.57±0.13
45.3%
Zh → En
Oracle length
0.8519±0.0007
100%
27.93±0.23
100%
Fixed ratio 1.2
0.8266±0.0010
0% (baseline)
23.65±0.21
0%
Table 1: Main LLaDA-8B+LoRA results on WMT22 with 32-step MED decoding. Values are mean ± std over three runs. Length Oracle uses the reference target length at decode time and is an upper bound. Gap closure is (method−Ratio)/(Oracle−Ratio) . Paired tests are in Appendix Table 11 .
System
Size
Setting
En → Zh
Zh → En
En → De
LLaDA-8B masked diffusion
Fixed ratio
8B
LoRA-SFT
83.45
82.66
71.70
Entropy-Valley
8B
LoRA-SFT
85.17
84.31
72.40
Oracle length †
8B
LoRA-SFT
86.10
85.19
73.82
Matched-data autoregressive baseline
LLaMA-3-8B + LoRA-SFT
8B
LoRA-SFT
85.07±0.03
83.68±0.07
81.19±0.11
Table 2: Matched-data COMET-22 calibration on WMT22. LLaDA rows show the Table 1 means over three runs scaled ×100 ; the matched AR row reports mean ± std over three runs after training on the same fine-tuning data and evaluating on the same test sets. † Oracle length supplies the reference target length at decode time and is an upper bound, not a deployable method.
Figure 4: Cross-backbone scope check using COMET-22 gap closure (%) for three masked-diffusion backbones and three directions. Gap closure is measured between Ratio and Length Oracle for each backbone–direction pair. Bars show means over three runs; error bars show standard deviations across runs. Full COMET-22 and sacreBLEU values are in Appendix G (Tables 17 and 18 ).
Figure 5: Quality need not track reference length. Target length error and COMET-22 on En → Zh WMT22 ( N=2037 ). Points show sentence scores; MAE values use the same outputs, and centroid heights use the main results in Table 1 .
Diagnostic
N
Ratio
EV
Placeholder retention
58
66.9%
89.1%
Number retention
290
77.6%
81.3%
r≥0.8 COMET
1005
0.8056
0.8402
r<0.6 COMET
236
0.8449
0.8503
Table 3: Coverage and length buckets on En → Zh. Retention rows measure whether literal source items such as placeholders and numbers are preserved. COMET rows group sentences by r , the reference target length divided by the source length under the LLaDA tokenizer. Appendix D gives the definitions, confidence intervals, and Zh → En companion rows.
Direction
Δ Adequacy
Δ Fluency
Preference
EV − Ratio
EV − Ratio
EV / Ratio / Tie
En → Zh
+0.18
+0.18
28 / 19 / 53
Zh → En
+0.50
+0.11
45 / 25 / 30
Table 4: Human evaluation on 100 stratified WMT22 sentences per direction. Score differences are EV − Ratio, averaged over three bilingual expert annotators; preference is the per-sentence majority vote.
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Value
Optimizer
AdamW
AdamW betas
(0.9,0.95)
Weight decay
0.01
Peak learning rate
2×10−4
Scheduler
Cosine decay
Warm-up
5% of training steps
Appendix
Table 5: Training and adaptation hyperparameters for the LLaDA and matched AR LoRA-SFT runs.
Range
K
Ratios
MAE
sBLEU
COMET
En → Zh (N=200)
Reported (narrow)
5
[0.70, 0.90]
2.71
38.73
0.8562
Medium
7
[0.60, 1.00]
2.84
38.49
0.8594
Wide
9
[0.50, 1.10]
3.06
38.17
0.8588
Full
12
[0.50, 1.20]
3.22
37.58
0.8577
Extra
15
[0.40, 1.50]
3.89
35.98
0.8476
Appendix
Table 6: Candidate-range control for Entropy-Valley on fixed 200-sentence WMT22 diagnostic subsets. The WMT19 training-corpus median provides a reference scale, while diagnostic range comparisons on WMT22 subsets informed the reported ratio grid. The En → Zh grid minimizes length MAE and gives the highest sacreBLEU, while the medium range gives the highest subset COMET; the En → De grid gives the highest subset COMET. The Zh → En subset benefits from a wider range.
Method
sacreBLEU
COMET-22
En → Zh (N=500, 32 steps)
Oracle
40.40
0.8617
Fixed 0.70
31.73
0.8114
Fixed 0.75
34.59
0.8208
Fixed 0.80
35.84
0.8281
Fixed 0.85
36.84
0.8354
Appendix
Table 7: Fixed-ratio sweep on fixed 500-sentence WMT22 diagnostic subsets. EV is compared with fixed ratios around the corpus median for all three directions. On Zh → En , the best post-hoc fixed ratio is 1.4 at 0.8390 COMET-22; EV reaches 0.8453 , exceeding it by +0.0063 COMET and closing 35.4% of the oracle-length gap on this subset.
Method
sacreBLEU
COMET-22
Cost
Oracle length
40.40
0.8617
1.00×
Fixed ratio 0.8
35.84
0.8281
1.00×
EV probe+decode
38.48
0.8557
1.15×
Decode 5 neighbours
37.85
0.8404
∼3.5×
Appendix
Table 8: Multi-candidate length selection on the same En → Zh WMT22 subset used in Table 7 (N=500, 32 steps). The alternative decodes five candidate canvas lengths obtained as integer offsets around the EV-selected length, {LEV−2,LEV−1,LEV,LEV+1,LEV+2} (with length collisions deduplicated), to completion and selects by average log-probability; its cost counts all completed decodes.
Dir.
Method
COMET
EV − method
Calls
Slots
Latency (s)
En → Zh
Ratio
0.833721
+0.010930
32.00
512.66
0.644
En → Zh
EV
0.844651
–
36.09
588.32
0.724
En → Zh
DAEDAL
0.828043
+0.016608([0.012954,0.020210];p<2×10−4)
34.58
1175.53
1.798
En → Zh
CAL
0.837897
+0.006754([0.003726,0.009880];p<2×10−4)
39.25
628.26
0.773
Zh → En
Ratio
0.818169
+0.016416
32.00
618.43
0.635
Zh → En
EV
0.834585
–
36.43
708.98
0.721
Appendix
Table 9: Direct diffusion length comparisons on WMT22 ( N=2037 per direction). Confidence intervals and paired bootstrap p -values are shown for DAEDAL and CAL. Calls and Slots are per-sentence averages; latency is measured in seconds per sentence in the reported setup. EV is above DAEDAL in both directions and CAL on En → Zh. The EV and CAL interval on Zh → En includes zero. EV uses fewer calls and slots than CAL, with lower latency in this setup.
Figure 6: Cost–quality Pareto. COMET-22 vs decoding steps T∈{2,4,8,16,32,64,128} on WMT22 ( N=2037 , one analyzed run). (A) En → Zh: EV is at least as high as Ratio at every T . (B) En → De: EV is higher at small T and slightly lower than Ratio at T≥64 . Oracle is a length oracle, not a decode oracle.
En → Zh
En → De
Steps
Oracle
EV
Ratio
Gap%
Oracle
EV
Ratio
Gap%
2
0.6975
0.7082
0.6861
194%
0.3942
0.4030
0.3915
426%
4
0.7856
0.7851
0.7644
98%
0.5074
0.5112
0.4912
123%
8
0.8290
0.8264
0.8058
89%
0.6060
0.6089
0.5862
115%
16
0.8520
0.8446
0.8265
71%
0.6873
0.6752
0.6683
36%
32
0.8592
0.8521
0.8325
73%
0.7417
0.7243
0.7209
16%
Appendix
Table 10: Full cost–quality Pareto on WMT22 ( N=2037 , one analyzed run). Gap% is computed relative to the Ratio and Oracle length columns at the same step budget; values can exceed 100% because Oracle fixes reference length but does not optimize decoding under small T .
Dir.
Comp.
Δ
95% CI
Boot. p
Wilc. p
En → Zh (A)
EV–Ratio
+0.0196
[+0.0166,+0.0226]
<10−4
4.1×10−32
En → Zh (A)
Oracle–EV
+0.0071
[+0.0046,+0.0096]
<10−4
1.3×10−14
En → Zh (A)
Oracle–Ratio
+0.0266
[+0.0233,+0.0300]
<10−4
3.4×10−58
En → De (A)
EV–Ratio
+0.0034
[−0.0016,+0.0086]
0.091
8.3×10−3
En → De (A)
Oracle–EV
+0.0173
[+0.0121,+0.0225]
<10−4
1.6×10−9
En → De (A)
Oracle–Ratio
+0.0208
[+0.0155,+0.0261]
<10−4
6.0×10−14
Appendix
Table 11: Sentence-level paired COMET-22 tests for LLaDA on WMT22 ( N=2037 throughout). Positive Δ means the first method is better. Paired bootstrap uses 10k resamples; Wilcoxon uses the signed-rank test with Pratt handling of zeros. The table reports run A for En → Zh and En → De , plus all three Zh → En runs. Oracle rows show the run A gap to the reference-length upper bound.
Direction
Method
T
Probe cap
Fwd cap
COMET-22
sacreBLEU
En → Zh, one analyzed run, WMT22 N=2037
En → Zh
Ratio 0.8
32
0
32
0.8325
36.53
En → Zh
Entropy-Valley
32
≤5
≤37
0.8521
38.56
En → Zh
Ratio 0.8
37
0
37
0.8334
36.66
En → Zh
Ratio 0.8
40
0
40
0.8333
36.71
Zh → En, one analyzed run, WMT22 N=2037
Appendix
Table 12: Forward-pass budget control. Ratio is evaluated at the default budget ( T=32 ), EV’s maximum total forward pass budget ( T=37 ), and a larger budget ( T=40 ). Duplicate integer candidate lengths can make EV’s realized budget smaller than the cap.
Category
N
Ratio
EV
Δ (pp)
95% CI (pp)
En → Zh — error-type preservation rate
Placeholder (#PRS_ORG#)
58
66.9%
89.1%
+22.1 ∗
[+12.4, +32.5]
Number / percentage / decimal
290
77.6%
81.3%
+3.7 ∗
[+1.4, +6.1]
Capitalized named entity (heuristic)
879
11.2%
11.9%
+0.7 ∗
[+0.0, +1.4]
En → Zh — length-compression buckets (LLaDA token ratio)
Bucket
N
Ratio COMET
EV COMET
Δ COMET
95% CI
Appendix
Table 13: Coverage and error categories. Top: source-side literal retention rate, averaged over three runs. Middle: En → Zh COMET-22 grouped by r=∣L∗∣/∣x∣ , the reference target length divided by source length under the LLaDA tokenizer. Bottom: Zh → En literal retention. Δ is in percentage points for retention rows; ∗ marks an interval whose unrounded lower endpoint is above zero.
Likely cause
N
Share
Mean Δ COMET
Overshoot beyond grid
129
21.6%
−0.0278
Under-compression
126
21.1%
−0.0206
Within-grid wrong pick
339
56.9%
−0.0247
Very short source
2
0.3%
—
Appendix
Table 14: Failure buckets for the 596 En → Zh cases where EV trails Ratio in one analyzed run (WMT22, N=2037 ). Buckets are assigned by mutually exclusive rules.
Schedule
COMET-22
Δ vs MED
Paired bootstrap p
MED (baseline)
0.8597
—
—
SIG-first
0.8603
+0.0006
0.62
Reverse-SIG
0.8523
−0.0075
<10−4
Hybrid MED → SIG, p=0.25
0.8582
−0.0015
0.21
Hybrid MED → SIG, p=0.50
0.8575
−0.0022
0.011
Hybrid MED → SIG, p=0.75
0.8591
−0.0007
0.28
Appendix
Table 15: Reveal-order controls on WMT22 En → Zh ( N=2037 , T=32 ) with reference length and the tokens-per-step schedule fixed. The six source-guided variants span 0.0081 COMET. Strict left-to-right and random order are additional controls and both score below MED. A paired bootstrap value is not reported for Strict L2R.
Category
N
SIG-first
MED
Δ (SIG − MED)
Dates
32
0.8652
0.8665
−0.0013
Enumeration
75
0.8560
0.8533
+0.0027
Named entities
280
0.8627
0.8629
−0.0002
Numbers
123
0.8679
0.8724
−0.0045
Overall
400
0.8640
0.8644
−0.0004
Appendix
Table 16: Source-guided order diagnostic on an En → Zh challenge subset ( N=400 , one analyzed run, T=32 MED vs. SIG-first under matched oracle length). SIG-first reveals high-source-dependence slots first; MED is the confidence-first schedule used in the main experiments.
Backbone
Direction
Oracle COMET
Ratio COMET
EV COMET
Δ EV − Ratio
COMET Gap closure
LLaDA-8B-Base (paper main results, § 4.2 ; reproduced for cross-backbone comparison)
LLaDA-8B-Base
En → Zh
0.8610±0.0013
0.8345±0.0017
0.8517±0.0006
+0.0172
64.9±7.4%
LLaDA-8B-Base
Zh → En
0.8519±0.0007
0.8266±0.0010
0.8431±0.0004
+0.0165
65.3±0.8%
LLaDA-8B-Base
En → De
0.7382±0.0090
0.7170±0.0090
0.7240±0.0078
+0.0070
33.0±8.4%
Dream-v0-Base-7B (Qwen2.5-7B continued-pretrained; Qwen2 tokenizer, 152 k vocab)
Dream-Base
En → Zh
0.8414±0.0020
0.8002±0.0016
0.8239±0.0004
+0.0238
57.7±3.1%
Appendix
Table 17: Cross-backbone COMET-22 results for Entropy-Valley (WMT22, N=2037 , three runs per aggregate cell, T=32 MED). Values are mean ± std across runs. COMET-22 gap closure is (EV−Ratio)/(Oracle−Ratio) per run, then mean ± std. EV is above Ratio in all six Dream-Base and DiffuLLaMA aggregate COMET cells; paired tests for every run give p<10−3 in all 18 Dream-Base and DiffuLLaMA comparisons, with positive 95% bootstrap confidence intervals. Absolute scores and closures vary by backbone.
Backbone
Direction
Oracle
Ratio
EV
LLaDA-8B-Base
En → Zh
40.81±0.23
36.72±0.22
38.57±0.13
LLaDA-8B-Base
Zh → En
27.93±0.23
23.65±0.21
25.28±0.33
LLaDA-8B-Base
En → De
22.55±0.77
20.73±0.68
21.55±0.85
Dream-Base
En → Zh
36.30±0.22
29.37±0.20
32.83±0.28
Dream-Base
Zh → En
27.24±0.28
23.56±0.04
25.78±0.20
Dream-Base
En → De
21.64±0.16
17.31±0.25
20.06±0.17
Appendix
Table 18: Companion sacreBLEU view of Table 17 (WMT22, N=2037 , three runs per cell). Values are mean ± std across runs.
Evaluation set
Pool
Ratio
EV
Δ COMET (95% CI)
WMT19 held out
50k
0.7428
0.7514
+0.0086[0.0034,0.0139]
WMT19 held out
200k
0.7386
0.7485
+0.0100[0.0050,0.0152]
FLORES devtest
50k
0.7398
0.7481
+0.0082[0.0020,0.0143]
FLORES devtest
200k
0.7315
0.7403
+0.0088[0.0024,0.0152]
Appendix
Table 19: De → Fr results for two nested training pools. WMT19 held out contains N=1512 sentences, and FLORES uses the full N=1012 De → Fr devtest. Both pools use a fixed 500 update budget and one candidate set for the direction. EV exceeds Ratio in all four settings, with positive paired confidence intervals; paired bootstrap and Wilcoxon tests are below 0.05 throughout. This is a robustness check under a fixed update budget, not a comparison of scaling with data size.
Figure 7: Human evaluation on En → Zh. (A) Per-annotator adequacy boxplots. (B) Sentence-level Δ COMET-22 vs 3-expert mean Δ Adequacy (EV − Ratio); Spearman ρ=0.637 ( p<0.001 ). The corresponding Zh → En correlation is reported in Table 20 .
A
B
C
Agg.
Panel A: En → Zh (N=100)
Δ Adequacy (EV − Ratio), mean
+0.19
+0.17
+0.19
+0.18
Δ Fluency (EV − Ratio), mean
+0.18
+0.20
+0.16
+0.18
Preference EV / Ratio / Tie
28/19/53
28/16/56
30/27/43
28/19/53
Wilcoxon p (Adequacy)
0.038∗
0.070
0.065
—
Wilcoxon p (Fluency)
0.056
0.035∗
0.135
—
Appendix
Table 20: Detailed human-evaluation statistics. The first three columns report annotator-level results. The aggregate preference uses per-sentence majority vote; aggregate Zh → En adequacy uses the paired Wilcoxon test on the three-expert mean.
Machine translation develops computational methods for converting text, speech, and visual content between languages while preserving meaning and purpose.