Diffusion large language models (dLLMs) have recently attracted significant attention for their ability to enhance diversity, controllability, and parallelism. However, their non-sequential, bidirectionally masked generation makes quality assessment difficult, underscoring the need for effective self-evaluation. In this work, we propose DiSE, a simple yet effective self-evaluation confidence quantification method for dLLMs. DiSE quantifies confidence by computing the probability of regenerating the tokens in the entire generated sequence, given the full context. This method enables more efficient and reliable quality assessment by leveraging token regeneration probabilities, facilitating both likelihood estimation and robust uncertainty quantification. Building upon DiSE, we further introduce a flexible-length generation framework, which adaptively controls the sequence length based on the model's self-assessment of its own output. We analyze and validate the feasibility of DiSE from the perspective of dLLM generalization, and empirically demonstrate that DiSE is positively correlated with both semantic coherence and answer accuracy. Extensive experiments on likelihood evaluation, uncertainty quantification, and flexible-length generation further confirm the effectiveness of the proposed DiSE. Project page: https://zhongzero.github.io/DiSE/
Figures & tables
Figure 1: A simplified illustration of self-evaluation confidence quantification methods for clarity. (a) Monte Carlo simulation approach for dLLMs. A total of Nmc simulations are performed. In the i -th simulation, a set of masked positions {maskji} is sampled. The tokens at these positions are replaced with mask tokens, and the model predicts the probability of correctly generating these tokens. The final estimation is obtained by aggregating the results across all Nmc simulations. (b) The proposed DiSE for dLLMs. The set of selected positions {Uj} is predefined. The model receives the entire sequence and estimates the regeneration probability of the tokens at {Uj} .
Figure 2: Generalization ability of dLLMs: Different tokens map from distinct start points to similar end points in the latent space.
Figure 3: Histogram and Cumulative distribution function (CDF) of GT token probability ranks.
Figure 4: Mean pairwise distribution distances for GT, mask, and random tokens using JS Divergence and Wasserstein Distance.
Figure 5: Differences between the DiSE scores of natural sentences and randomized sentences using the LLaDA-Instruct-8B model under four selection modes: ‘full’ (entire sentence), ‘first-10’ (first 10 tokens), ‘mid-10’ (10 tokens from the middle) and ‘last-10’ (last 10 tokens). Each subfigure contains 15 blocks, representing 15 sampled sentences. All blocks are shown in green (difference >0 ), indicating that natural sentences consistently achieve higher DiSE scores than randomized sentences.
Figure 6: Comparison between the DiSE scores of correct and incorrect answers across four datasets using the LLaDA-Instruct-8B model under two selection modes ‘full’ and ‘last-10’.
Figure 7: Illustration of the flexible-length dLLM generation framework with DiSE versus fixed-length generation. (a) Fixed-length generation baseline. (b) Flexible-length generation with DiSE.
Method
ARC-Challenge
GPQA
# NFE
LLaDA-Instruct-8B
MC, Nmc=1
0.306
0.212
1
MC, Nmc=32
0.478
0.286
32
DiSE (ours)
0.542
0.301
1
LLaDA-1.5-8B
MC, Nmc=1
0.311
0.203
1
MC, Nmc=32
0.488
0.275
32
DiSE (ours)
0.567
0.299
1
Table 1: Conditional likelihood estimation results on ARC-Challenge and GPQA. The table compares the proposed DiSE against the Monte Carlo simulation baseline with varying Nmc , and also includes a comparison with the probability estimates from auto-regressive LLMs. The last column reports the average number of model forward passes per computation.
Countdown
GSM8K
MATH500
SVAMP
Avg. ROC-AUC ↑
Method / Gen Len
128
256
512
128
256
512
128
256
512
128
256
512
LLaDA-Instruct-8B
MC, Nmc=1
0.524
0.520
0.528
0.539
0.513
0.540
0.497
0.541
0.532
0.563
0.575
0.509
0.532
MC, Nmc=32
0.595
0.534
0.558
0.590
0.552
0.595
0.528
0.578
0.531
0.616
0.551
0.647
0.573
DiSE (ours)
0.578
0.521
0.622
0.633
0.644
0.658
0.611
0.634
0.604
0.688
0.692
0.755
0.637
LLaMA perplexity
0.574
0.419
0.392
0.675
0.605
0.577
0.575
0.637
0.551
0.686
0.650
0.590
0.578
LLaDA-1.5-8B
MC, Nmc=1
0.525
0.588
0.528
0.516
0.559
0.525
0.558
0.514
0.525
0.562
0.466
0.554
0.535
Table 2: ROC-AUC scores for uncertainty quantification on the Countdown, GSM8K, MATH500 and SVAMP datasets with varing generation lengths. The table compares Monte Carlo simulation baseline with varying Nmc , the proposed DiSE, and the perplexity calculation using the auto-regressive model LLaMA3-Instruct-8B. The last column reports the average ROC-AUC scores across the preceding 12 settings.
Figure 8: Qualitative example of uncertainty quantification with four generated answers using LLaDA-Instruct-8B.
Figure 9: Ablation study of different DiSE selection modes for uncertainty quantification using LLaDA-Instruct-8B with a generation length of 512.
Countdown
GSM8K
MATH500
SVAMP
Avg. Accuracy
Method / Base Len
128
256
512
128
256
512
128
256
512
128
256
512
LLaDA-Instruct-8B
Baseline
26.17
15.23
12.50
68.01
76.65
79.23
26.20
32.80
36.80
84.67
85.00
83.67
52.24
Baseline (Max Len)
25.00
16.41
15.62
69.29
76.80
78.85
25.60
31.60
36.40
85.33
84.67
83.00
52.38
DiSE-flexible (ours)
27.73
18.36
15.62
70.96
79.68
79.30
26.00
33.60
36.60
87.33
86.00
84.33
53.79
LLaDA-1.5-8B
Baseline
24.22
15.62
17.19
70.51
77.48
79.53
26.80
34.00
36.80
87.00
84.67
86.67
53.37
Baseline (Max Len)
24.22
17.58
17.58
71.95
78.77
79.53
25.80
34.20
37.00
86.33
83.00
86.33
53.52
Table 3: Results of flexible-length dLLM generation with DiSE on the Countdown, GSM8K, MATH500, and SVAMP datasets with varying base lengths. The table shows two fixed-length baselines: Baseline , generating sequences of base length L , and Baseline (Max Len) , generating sequences of length L+Mmax . These are compared with the proposed flexible-length generation with DiSE (DiSE-flexible). The final column reports the average accuracy across the preceding 12 configurations.
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
Countdown
GSM8K
MATH500
SVAMP
Avg. Accuracy
Method / Gen Len
128
256
512
128
256
512
128
256
512
128
256
512
LLaDA-Instruct-8B
Baseline
26.17
15.23
12.50
68.01
76.65
79.23
26.20
32.80
36.80
84.67
85.00
83.67
52.24
MC, Nmc=1
24.61
21.48
17.19
68.84
78.17
80.59
25.80
33.80
36.40
84.67
84.00
85.00
53.38
MC, Nmc=32
29.69
21.88
16.41
71.11
78.70
82.79
27.60
34.80
36.20
86.33
85.67
86.67
54.82
DiSE (ours)
30.86
24.22
27.34
73.01
82.41
83.02
29.80
34.60
38.20
88.33
87.00
90.00
57.40
LLaMA perplexity
30.86
17.19
11.33
74.22
79.61
81.20
28.60
35.40
34.80
88.33
86.67
85.67
54.49
Appendix
Table S1: Best-of-N sampling results for uncertainty quantification on the Countdown, GSM8K, MATH500, and SVAMP datasets with varying generation lengths. The table compares the baseline without best-of-N sampling, Monte Carlo simulation with varying Nmc , the proposed DiSE, and the perplexity calculation using the auto-regressive model LLaMA3-Instruct-8B. The last column reports the average accuracy across the preceding 12 settings.
Figure S1: Additional qualitative examples of uncertainty quantification using LLaDA-Instruct-8B. DiSE assigns higher scores to correct answers and lower scores to incorrect answers, while the Monte Carlo simulation ( Nmc=32 ) produces scores that do not consistently reflect correctness.
Countdown
GSM8K
MATH500
SVAMP
Avg. ROC-AUC ↑
Method / Gen Len
128
256
512
128
256
512
128
256
512
128
256
512
LLaDA-Instruct-8B
DiSE (full)
0.616
0.672
0.698
0.597
0.585
0.560
0.514
0.555
0.517
0.665
0.549
0.571
0.592
DiSE (last-10)
0.578
0.521
0.622
0.633
0.644
0.658
0.611
0.634
0.604
0.688
0.692
0.755
0.637
LLaDA-1.5-8B
DiSE (full)
0.591
0.664
0.681
0.593
0.569
0.546
0.489
0.590
0.532
0.630
0.574
0.552
0.584
DiSE (last-10)
0.610
0.471
0.586
0.610
0.616
0.613
0.606
0.553
0.533
0.599
0.629
0.677
0.592
Appendix
Table S2: Additional ROC-AUC results for uncertainty quantification to investigate the impact of different selection modes on performance. We evaluate two selection modes ‘full’ and ‘last-10’. The table reports ROC-AUC scores across the Countdown, GSM8K, MATH500, and SVAMP datasets with varying generation lengths, as well as the average ROC-AUC scores over all settings.
Countdown
GSM8K
MATH500
SVAMP
Avg. Accuracy
Method / Gen Len
128
256
512
128
256
512
128
256
512
128
256
512
LLaDA-Instruct-8B
DiSE (full)
30.86
28.52
27.34
71.87
79.76
79.53
27.20
34.60
34.20
87.67
85.33
87.00
56.16
DiSE (last-10)
30.86
24.22
27.34
73.01
82.41
83.02
29.80
34.60
38.20
88.33
87.00
90.00
57.40
LLaDA-1.5-8B
DiSE (full)
27.34
25.00
32.81
72.33
79.45
80.06
24.80
37.20
38.00
88.33
86.67
85.00
56.42
DiSE (last-10)
29.30
17.97
28.91
74.53
81.96
83.55
28.60
34.40
37.40
88.00
86.33
87.67
56.55
Appendix
Table S3: Additional best-of-N sampling results for uncertainty quantification to investigate the impact of different selection modes on performance. We evaluate two selection modes ‘full’ and ‘last-10’. The table reports accuracy across the Countdown, GSM8K, MATH500, and SVAMP datasets with varying generation lengths, as well as the average accuracy over all settings.
Countdown
GSM8K
MATH500
SVAMP
Avg. Accuracy
Avg. # NFE
Avg. Time(s)
Method / Base Len
128
256
512
128
256
512
128
256
512
128
256
512
Baseline
26.17
15.23
12.50
68.01
76.65
79.23
26.20
32.80
36.80
84.67
85.00
83.67
52.24
149.3
3.27
DiSE-flexible (K=2)
27.34
18.36
16.02
70.43
79.30
79.23
26.40
34.00
36.60
87.33
86.00
84.67
53.81
182.3
3.86
DiSE-flexible (K=3)
27.34
17.97
15.62
70.74
79.61
79.23
25.80
33.80
36.60
87.33
86.00
84.33
53.70
199.3
4.18
DiSE-flexible (K=4)
27.73
18.36
15.62
70.96
79.68
79.30
26.00
33.60
36.60
87.33
86.00
84.33
53.79
215.3
4.55
Appendix
Table S4: Ablation study on flexible-length dLLM generation using LLaDA-Instruct-8B, analyzing the impact of different patience values K on performance. The table reports accuracy on the Countdown, GSM8K, MATH500, and SVAMP datasets with varying base lengths, along with the average accuracy, the average number of model forward passes and average time for each configuration.
Countdown
GSM8K
MATH500
SVAMP
Avg. Accuracy
Avg. # NFE
Avg. Time(s)
Method / Base Len
128
256
512
128
256
512
128
256
512
128
256
512
Baseline
24.22
15.62
17.19
70.51
77.48
79.53
26.80
34.00
36.80
87.00
84.67
86.67
53.37
149.3
3.25
DiSE-flexible (K=2)
24.61
17.19
19.14
72.40
79.23
80.06
27.40
35.60
37.40
87.33
84.67
87.00
54.34
182.0
3.84
DiSE-flexible (K=3)
24.61
19.14
20.70
72.48
79.45
80.06
27.80
35.40
37.40
87.00
84.67
87.00
54.64
198.9
4.20
DiSE-flexible (K=4)
26.17
19.53
22.27
72.33
79.53
80.06
27.20
35.60
37.40
87.00
85.00
87.00
54.92
214.7
4.53
Appendix
Table S5: Ablation study on flexible-length dLLM generation using LLaDA-1.5-8B, analyzing the impact of different patience values K on performance. The table reports accuracy on the Countdown, GSM8K, MATH500, and SVAMP datasets with varying base lengths, along with the average accuracy, the average number of model forward passes and average time for each configuration.
Figure S2: Ablation study on the Countdown dataset using LLaDA-Instruct-8B with base length L=512 for flexible-length dLLM generation with DiSE, examining the effects of different patience K and mask sizes D on performance. The figure presents both accuracy and the average number of model forward passes for each configuration.
Figure S3: Ablation study on the Countdown dataset using LLaDA-1.5-8B with base length L=512 for flexible-length dLLM generation with DiSE, examining the effects of different patience K and mask sizes D on performance. The figure presents both accuracy and the average number of model forward passes for each configuration.
Figure S4: Comparison between our method and DAEDAL on the GSM8K and MATH500 datasets using LLaDA-Instruct-8B. The numbers in parentheses on the x-axis indicate the maximum output length for each setting.
Method
ARC-Challenge
GPQA
# NFE
Dream-Instruct-7B
MC, Nmc=1
0.290
0.223
1
MC, Nmc=32
0.316
0.259
32
DiSE (ours)
0.472
0.297
1
Appendix
Table S6: Conditional likelihood estimation results on ARC-Challenge and GPQA using Dream-Instruct-7B. The table compares the proposed DiSE against the Monte Carlo simulation baseline with varying Nmc . The last column reports the average number of model forward passes per computation.
Countdown
GSM8K
MATH500
SVAMP
Avg. ROC-AUC ↑
Method / Gen Len
128
256
128
256
128
256
128
256
Dream-Instruct-7B
MC, Nmc=1
0.463
0.548
0.473
0.503
0.538
0.464
0.510
0.551
0.506
MC, Nmc=32
0.600
0.482
0.483
0.497
0.471
0.576
0.469
0.467
0.506
DiSE (ours)
0.651
0.505
0.591
0.530
0.543
0.445
0.604
0.482
0.544
Appendix
Table S7: Additional ROC-AUC results for uncertainty quantification using Dream-Instruct-7B. The table reports ROC-AUC scores across the Countdown, GSM8K, MATH500, and SVAMP datasets with varying generation lengths, as well as the average ROC-AUC scores over all settings.
Figure S5: Boxplot of Pairwise Distribution Distances for GT, mask and random tokens using JS Divergence and Wasserstein Distance.
Figure S6: Cumulative distribution function (CDF) of GT token probability ranks for fixed sequence and position. (Part 1)
Figure S7: Cumulative distribution function (CDF) of GT token probability ranks for fixed sequence and position. (Part 2)
Figure S8: More examples for distributions of GT, mask, and random tokens and their comparison.
Diffusion language models (DLMs) alleviate the inherent latency bottleneck of autoregressive (AR) large language models (LLMs), but their degraded generation quality limits practical applicability. Although knowledge distillation (KD) can be a promising direction for improving performance, we empirically find that naively applying conventional KD yields only marginal gains, or even degrades generation quality. Based on these observations, we propose a novel self-distillation framework for DLMs, namely SelFusion. To enable effective KD without an external teacher model, SelFusion performs two forward passes with different masking levels, defining the hard mode with a larger masking probability and the easy mode with a smaller masking probability. However, the easy mode is not always more accurate than the hard mode and can be overconfident on incorrect tokens. Thus, we introduce bidirectional KD between the two modes, which can dynamically determine the distillation direction based on token-level correctness. Experimental results on instruction-following tasks show that the proposed self-distillation substantially outperforms other KD methods with external LLM and DLM teachers. In many configurations, the student trained with SelFusion even surpasses the performance of the LLM teacher, providing a practical path toward improving DLM generation quality. Source code can be found at https://github.com/scai-research/SelFusion_official
Hyeongsoo Lim, Jinyoung Kim, Eunseo Seo +2
Department of Artificial Intelligence, Chung-Ang University
While Diffusion Large Language Models (dLLMs) offer structural advantages for global planning, efficiently verifying that they arrive at correct answers via valid reasoning traces remains a critical challenge. In this work, we propose a geometric perspective: Reasoning on the Manifold. We hypothesize that valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, whereas invalid paths exhibit off-manifold drift. To operationalize this, we introduce Bidirectional Manifold Consistency (BMC), a training-free, unsupervised metric that quantifies the stability of the generated sequence through a forward-masking and backward-reconstruction cycle. Empirically, we demonstrate BMC's versatility across the full reasoning lifecycle: (1) in Diagnosis, it serves as a robust discriminator of solution validity without ground truth answer; (2) in Inference, it enables rejection resampling to effectively concentrate computational resources on complex reasoning tasks; and (3) in Alignment, it functions as a dense geometric reward that transforms sparse outcome supervision into fine-grained guidance, empowering models to self-evolve beyond standard baselines. Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.
Jiaoyang Ruan, Xin Gao, Yinda Chen +5
Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China · Shanghai Artificial Intelligence Laboratory, Shanghai, China · University of Science and Technology of China, Hefei, China +1
Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to auto-regressive (AR) models, offering greater expressive capacity and potential for parallel generation and faster inference. However, open-source dLLMs remain immature, lagging behind AR models in both efficiency and quality. We identify an underexplored property of dLLMs: token-wise redundancy in bi-directional self-attention. Self-attention activations are highly correlated across tokens, and temporal changes in query representations can predict redundancy in corresponding key, value, and output activations. We introduce DARE, with two complementary mechanisms: DARE-KV, which reuses cached key-value (KV) activations, and DARE-O, which reuses output activations to reduce redundant computation while preserving quality. DARE achieves up to 1.20x per-layer latency reduction and reuses up to 87% of attention activations, with negligible degradation on reasoning and code-generation benchmarks. DARE-KV and DARE-O incur average performance drops of only 2.0% and 1.2%, respectively. Combined with techniques such as prefix caching and Fast-dLLM, DARE provides additive gains without retraining. These results establish token-wise reuse as an effective strategy for improving the efficiency of diffusion-based LLMs while preserving generation fidelity. Code: https://github.com/enyac-group/DARE
Natalia Frumkin, Bokun Wang, Hung-Yueh Chiang +3
Chandra Family Department of Electrical and Computer Engineering The University of Texas at Austin · Cornell University