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arxiv: 2604.10567 · v1 · submitted 2026-04-12 · 💻 cs.CL · cs.AI

Recognition: unknown

Early Decisions Matter: Proximity Bias and Initial Trajectory Shaping in Non-Autoregressive Diffusion Language Models

Jiyeon Kim , Sungik Choi , Yongrae Jo , Moontae Lee , Minjoon Seo
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:10 UTC · model grok-4.3

classification 💻 cs.CL cs.AI
keywords diffusion language modelsnon-autoregressive decodingproximity biasdenoising ordererror propagationinitial trajectoryreasoning tasksplanning tasks
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The pith

Proximity bias in non-autoregressive diffusion language models makes the full generation trajectory depend on the position of the first unmasked token.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper analyzes inference dynamics in diffusion language models during non-autoregressive decoding. It identifies a strong proximity bias where the denoising order concentrates on spatially adjacent tokens rather than spreading out. This creates local error propagation, so overall output quality hinges on which token is chosen for initial unmasking. The authors introduce a lightweight planner to guide early selections and end-of-sequence temperature annealing, which improves results on reasoning and planning tasks with little added cost. A sympathetic reader would care because this explains a core limitation of parallel generation and offers a practical fix.

Core claim

In confidence-based non-autoregressive generation for diffusion language models, the denoising order exhibits a strong proximity bias that concentrates unmasking on spatially adjacent tokens. This local dependency produces spatial error propagation, rendering the entire generation trajectory critically contingent on the initial unmasking position. A minimal-intervention method that employs a lightweight planner for early token selection and end-of-sequence temperature annealing delivers substantial gains over heuristic baselines on reasoning and planning tasks without meaningful overhead.

What carries the argument

The proximity bias in denoising order, which forces unmasking to favor nearby tokens and makes the starting unmasking position determine the quality of the full spatial trajectory.

If this is right

  • The quality of non-autoregressive outputs is largely decided by the first few unmasking decisions rather than later refinement steps.
  • Error propagation remains spatially local because the denoising order avoids distant tokens.
  • Inference-time guidance of early positions can lift performance on complex tasks without retraining the underlying model.
  • Temperature annealing at the sequence end stabilizes final tokens once the trajectory is set by initial choices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The bias may arise from how diffusion models are trained on ordered data, so altering training order or objectives could reduce it at the source.
  • Similar spatial concentration effects might appear in other iterative non-autoregressive generators outside the diffusion setting.
  • Hybrid systems that mix limited autoregressive steps with diffusion could bypass the bias by handling the critical early tokens sequentially.
  • The planner approach might scale to larger models but could require task-specific tuning to avoid introducing its own local traps.

Load-bearing premise

The observed proximity bias is the dominant cause of poor non-autoregressive performance and a lightweight planner plus temperature annealing will correct it reliably across tasks without new failure modes or significant overhead.

What would settle it

If experiments with random initial unmasking positions show no consistent variation in final generation quality, or if the planner-plus-annealing method produces no measurable improvement on a new set of reasoning tasks, the claim that proximity bias is the key failure mode would be falsified.

Figures

Figures reproduced from arXiv: 2604.10567 by Jiyeon Kim, Minjoon Seo, Moontae Lee, Sungik Choi, Yongrae Jo.

Figure 1
Figure 1. Figure 1: (a) Confidence-based sampling in non-autoregressive decoding suffers from premature constriction of the generation window due to proximity bias, where neighboring tokens accumulate confidence sequentially. This leads to spatial error propagation, making early unmasking decisions decisive for the entire trajectory. (b) We introduce a lightweight planner and EOS temperature annealing to strategically guide i… view at source ↗
Figure 2
Figure 2. Figure 2: Performance in confidence-based non-autoregressive de￾coding across different diffusion timesteps(T) when the generation length(L) is fixed at 256. 0 20 40 60 80 100 120 Decoding Steps 50 100 150 200 250 Token Position Index Unmasked Position (front) Unmasked Position (back) Ratio of EOS 0 10 20 30 40 50 60 70 Ratio of EOS (%) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Unmasked token position index and average ratio of predicting EOS token across diffusion timesteps (x-axis) when evaluating on GSM8K testset with T = 128, L = 256. Since two tokens are unmasked simultaneously at each step, we plot both positions, distinguishing between the earlier(front) and later(back) tokens in the sequence. Token position index and ratio of EOS is averaged over all test instances. compu… view at source ↗
Figure 4
Figure 4. Figure 4: Pass@k accuracy on GSM8K with a fixed budget of T = 32 across different k(x-axis). The impact of uniform sam￾pling in Position Selection injected at different decoding steps is compared with token-level Temperature Sampling. The solid red line represents randomness applied only at the initial step, while dashed red lines indicate delayed randomness introduced at inter￾mediate steps. The dashed black line d… view at source ↗
Figure 5
Figure 5. Figure 5: Accuracy for randomness introduced via Position Sam￾pling and Temperature Sampling, categorized into Correct Paths, Incorrect Paths, and their union. Error bars represent 95% boot￾strapped confidence intervals. the token value greedily at all steps. In both cases, all the parameters including timesteps, are held constant [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Unmasked token position index and average ratio of predicting EOS token across diffusion timesteps (x-axis) when evaluating with T = 32, L = 256. Instruct demonstrate that applying randomness to the initial position steers the generation trajectory significantly better than token-level sampling at all steps. 0 20 40 60 80 100 120 Decoding Steps 0 50 100 150 200 250 Token Position Index Unmasked Position (f… view at source ↗
Figure 11
Figure 11. Figure 11: Unmasked token position index and average ra￾tio of predicting EOS token across diffusion timesteps (x-axis) when evaluating Dream 7B Instruct on GSM8K testset with T = 128, L = 256. 0 5 10 15 20 25 30 Decoding Steps 50 100 150 200 250 Token Position Index Unmasked Position Ratio of EOS 0 20 40 60 80 100 Ratio of EOS (%) [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 9
Figure 9. Figure 9: Top 1 probability predicted at each diffusion timestep(x￾axis) for each token position(y-axis) in Non-Autoregressive decod￾ing under tight budget(T = 32). 0 20 40 60 80 100 120 Diffusion timesteps 0 50 100 150 200 250 Token position 0.2 0.4 0.6 0.8 1.0 prob [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Top 1 probability predicted at each diffusion timestep(x￾axis) for each token position(y-axis) in Semi-Autoregressive de￾coding under lenient budget(T = 128). struct. For computational efficiency, we use a scaled-down 0 20 40 60 80 100 120 Decoding Steps 50 100 150 200 250 Token Position Index Unmasked Position (front) Unmasked Position (back) Ratio of EOS 0 20 40 60 80 100 Ratio of EOS (%) [PITH_FULL_IM… view at source ↗
Figure 13
Figure 13. Figure 13: Pass@k accuracy of Dream 7B Instruct on GSM8K with a fixed budget of T = 32 across different k(x-axis). The impact of uniform sampling in Position Selection injected at dif￾ferent decoding steps is compared with token-level Temperature Sampling. Total Correct Paths Incorrect Paths 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Accuracy(%) Position Sampling Temperature Sampling [PITH_FULL_IMAGE:figures/full_fig_p017… view at source ↗
Figure 16
Figure 16. Figure 16: Unmasked token position index and average ratio of pre￾dicting EOS token across diffusion timesteps (x-axis) when evaluat￾ing LLaDA 8B Instruct on Countdown with T = 128, L = 256. 0 20 40 60 80 100 120 Decoding Steps 0 50 100 150 200 250 Token Position Index Unmasked Position (front) Unmasked Position (back) Ratio of EOS 0 20 40 60 80 100 Ratio of EOS (%) [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Unmasked token position index and average ratio of predicting EOS token across diffusion timesteps (x-axis) when evaluating LLaDA 8B Instruct on Sudoku with T = 128, L = 256. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Accuracy of LLaDA 7B Instruct on MATH for random￾ness introduced via Position Sampling and Temperature Sampling, categorized into Correct Paths, Incorrect Paths, and their union. Error bars represent 95% bootstrapped confidence intervals. more effective than continuous token-level sampling. More￾over, early denoising decisions rigidly constrain the final generation, demonstrating that this disproportionat… view at source ↗
Figure 19
Figure 19. Figure 19: Performance on each task across different numbers of candidates P. F.2. Task-dependent effect of randomness in position selection and token prediction Although our approach significantly improves performance over all the baselines, Sudoku is an exception. We analyze that the impact of randomness varies significantly by task structure. Across all tasks, introducing positional random￾ness at every step yiel… view at source ↗
read the original abstract

Diffusion-based language models (dLLMs) have emerged as a promising alternative to autoregressive language models, offering the potential for parallel token generation and bidirectional context modeling. However, harnessing this flexibility for fully non-autoregressive decoding remains an open question, particularly for reasoning and planning tasks. In this work, we investigate non-autoregressive decoding in dLLMs by systematically analyzing its inference dynamics along the temporal axis. Specifically, we uncover an inherent failure mode in confidence-based non-autoregressive generation stemming from a strong proximity bias-the tendency for the denoising order to concentrate on spatially adjacent tokens. This local dependency leads to spatial error propagation, rendering the entire trajectory critically contingent on the initial unmasking position. Leveraging this insight, we present a minimal-intervention approach that guides early token selection, employing a lightweight planner and end-of-sequence temperature annealing. We thoroughly evaluate our method on various reasoning and planning tasks and observe substantial overall improvement over existing heuristic baselines without significant computational overhead.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper analyzes non-autoregressive decoding dynamics in diffusion language models (dLLMs). It identifies a proximity bias in confidence-based token selection, where denoising concentrates on spatially adjacent tokens, causing spatial error propagation and making the full generation trajectory dependent on the initial unmasking position. The authors propose a minimal-intervention fix consisting of a lightweight planner for early token selection and end-of-sequence temperature annealing, claiming substantial improvements over heuristic baselines on reasoning and planning tasks with negligible overhead.

Significance. If the proximity bias is shown to be causal and the proposed planner plus annealing reliably corrects it across tasks, the work would provide a practical advance for non-autoregressive generation in dLLMs, enabling better parallel decoding for complex reasoning without heavy compute. The focus on inference-time dynamics offers a useful diagnostic lens, though the absence of detailed quantitative support and causal tests in the current presentation limits the assessed impact.

major comments (2)
  1. [analysis of denoising dynamics] The central claim that proximity bias is the mechanistic driver of spatial error propagation (abstract and analysis of denoising order) rests on observational evidence of adjacent-token concentration. A controlled intervention that breaks spatial locality while holding confidence scores fixed (e.g., re-ranking high-confidence candidates with an explicit anti-proximity penalty or uniform sampling over top-confidence tokens) is required to establish causality rather than correlation; without it, early-step confidence miscalibration or data-distribution effects remain plausible alternative drivers.
  2. [experimental evaluation] The abstract states 'substantial overall improvement' and 'thorough evaluation' on reasoning/planning tasks, yet provides no quantitative metrics, error bars, ablation tables, or experimental-setup details. If the full manuscript similarly omits these (or reports only point estimates without controls for the planner's contribution), the empirical support for the method's effectiveness and the claim that it avoids new failure modes cannot be assessed.
minor comments (2)
  1. Define the precise architecture and training of the 'lightweight planner' (e.g., parameter count, input features, whether it is task-specific) so readers can reproduce the minimal-intervention claim.
  2. Clarify how end-of-sequence temperature annealing interacts with the planner and whether it is applied only at the final step or throughout the trajectory.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our analysis of denoising dynamics in diffusion language models. We address each major comment below with clarifications and planned revisions to strengthen the causal claims and empirical presentation.

read point-by-point responses

  1. Referee: The central claim that proximity bias is the mechanistic driver of spatial error propagation (abstract and analysis of denoising order) rests on observational evidence of adjacent-token concentration. A controlled intervention that breaks spatial locality while holding confidence scores fixed (e.g., re-ranking high-confidence candidates with an explicit anti-proximity penalty or uniform sampling over top-confidence tokens) is required to establish causality rather than correlation; without it, early-step confidence miscalibration or data-distribution effects remain plausible alternative drivers.

    Authors: We acknowledge that the current evidence for proximity bias as the primary driver is observational. To establish causality, we will add a controlled ablation in the revised manuscript: during early denoising steps, we will re-rank the top-confidence tokens using an explicit anti-proximity penalty (while preserving the original confidence values) and compare generation trajectories and error propagation against the baseline selection. We will also analyze the planner's intervention as a direct disruption of spatial locality in initial unmasking. This should help rule out alternative explanations such as confidence miscalibration. revision: yes

  2. Referee: The abstract states 'substantial overall improvement' and 'thorough evaluation' on reasoning/planning tasks, yet provides no quantitative metrics, error bars, ablation tables, or experimental-setup details. If the full manuscript similarly omits these (or reports only point estimates without controls for the planner's contribution), the empirical support for the method's effectiveness and the claim that it avoids new failure modes cannot be assessed.

    Authors: The full manuscript includes quantitative comparisons on reasoning and planning tasks along with ablation studies on the planner and annealing components. To improve transparency, we will revise the experimental section to report error bars across multiple random seeds, expanded ablation tables that isolate the planner's contribution from annealing, and additional details on experimental setups and hyperparameters. We will also include analysis addressing potential new failure modes introduced by the interventions. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on empirical observation of denoising order, not self-referential definitions or fitted predictions

full rationale

The paper identifies proximity bias through direct inspection of confidence-based token selection sequences in non-autoregressive diffusion decoding. This is presented as an observed pattern in inference dynamics rather than a quantity derived from or defined in terms of the error propagation it is said to cause. The subsequent lightweight planner and temperature annealing are introduced as a minimal intervention motivated by the observation, without any equations that reduce the intervention's success metric to the bias measurement by construction. No self-citation chains, uniqueness theorems, or ansatzes are invoked to justify core premises. The analysis remains self-contained against external task benchmarks and does not rename known results or treat fitted parameters as predictions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claim appears to rest on empirical observation of model behavior rather than new theoretical constructs.

pith-pipeline@v0.9.0 · 5481 in / 1114 out tokens · 36863 ms · 2026-05-10T15:10:04.320496+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

17 extracted references · 5 canonical work pages · 4 internal anchors

  1. [1]

    Training Verifiers to Solve Math Word Problems

    URL https://openreview.net/forum? id=WBcBhT1NKO. Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al. Language models are few-shot learners. Advances in neural information processing systems, 33: 1877–1901, 2020. Campbell, A., Benton, J., De Bortoli, V ., Rainforth, T., Deli- ...

    work page internal anchor Pith review Pith/arXiv arXiv 1901

  2. [2]

    Hendrycks, D., Burns, C., Kadavath, S., Arora, A., Basart, S., Tang, E., Song, D., and Steinhardt, J

    URL https://openreview.net/forum? id=j1tSLYKwg8. Hendrycks, D., Burns, C., Kadavath, S., Arora, A., Basart, S., Tang, E., Song, D., and Steinhardt, J. Measuring mathematical problem solving with the MATH dataset. InThirty-fifth Conference on Neural Information Process- ing Systems Datasets and Benchmarks Track (Round 2),

  3. [3]

    Ho, J., Jain, A., and Abbeel, P

    URL https://openreview.net/forum? id=7Bywt2mQsCe. Ho, J., Jain, A., and Abbeel, P. Denoising diffusion proba- bilistic models.Advances in neural information process- ing systems, 33:6840–6851, 2020. Israel, D. M., den Broeck, G. V ., and Grover, A. Ac- celerating diffusion LLMs via adaptive parallel decod- ing. InThe Thirty-ninth Annual Conference on Neur...

    2020

  4. [4]

    Diffusion Language Models Know the Answer Before Decoding

    URL https://openreview.net/forum? id=cznTlh7Msz. Kim, J., Shah, K., Kontonis, V ., Kakade, S. M., and Chen, S. Train for the worst, plan for the best: Under- standing token ordering in masked diffusions. InForty- second International Conference on Machine Learning, 2025a. URL https://openreview.net/forum? id=DjJmre5IkP. Kim, S. H., Hong, S., Jung, H., Par...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  5. [5]

    org/CorpusID:276161145

    URL https://api.semanticscholar. org/CorpusID:276161145. Sahoo, S. S., Arriola, M., Gokaslan, A., Marroquin, E. M., Rush, A. M., Schiff, Y ., Chiu, J. T., and Kuleshov, V . Simple and effective masked diffusion language mod- els. InThe Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https: //openreview.net/forum?id=L4ua...

    2024

  6. [6]

    DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

    URL https://openreview.net/forum? id=HvIRFV0J90. Shao, Z., Wang, P., Zhu, Q., Xu, R., Song, J., Bi, X., Zhang, H., Zhang, M., Li, Y ., Wu, Y ., et al. Deepseekmath: Push- ing the limits of mathematical reasoning in open language models.arXiv preprint arXiv:2402.03300, 2024. Shi, J., Han, K., Wang, Z., Doucet, A., and Titsias, M. Simplified and generalized...

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  7. [7]

    wd1: Weighted policy optimization for reasoning in diffusion language models.arXiv preprint arXiv:2507.08838,

    URL https://openreview.net/forum? id=PxTIG12RRHS. Tang, X., Dolga, R., Yoon, S., and Bogunovic, I. wd1: Weighted policy optimization for reasoning in diffusion language models.ArXiv, abs/2507.08838,

    work page arXiv

  8. [8]

    LLaMA: Open and Efficient Foundation Language Models

    URL https://api.semanticscholar. org/CorpusID:280280745. Touvron, H., Lavril, T., Izacard, G., Martinet, X., Lachaux, M.-A., Lacroix, T., Rozi`ere, B., Goyal, N., Hambro, E., Azhar, F., et al. Llama: Open and efficient foundation lan- guage models.arXiv preprint arXiv:2302.13971, 2023. Wagenmaker, A., Nakamoto, M., Zhang, Y ., Park, S., Yagoub, W., Nagaba...

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  9. [9]

    Subsequent studies further refined the formulation of discrete diffusion

    to discrete state spaces by defining categorical for- ward noising and reverse denoising processes. Subsequent studies further refined the formulation of discrete diffusion. Campbell et al. (2022) modeled the forward and backward processes over discrete variables as continuous-time Markov chains, enabling principled derivation of training objectives and s...

    2022

  10. [10]

    Start with the largest number, 89, and try to use it in the expression

  11. [11]

    Let’s try: - 89 - 37 = 52 - 52 - 41 = 11 So, the expression is 89 - 37 - 41 = 11

    Use the subtraction operation to get the target number 11. Let’s try: - 89 - 37 = 52 - 52 - 41 = 11 So, the expression is 89 - 37 - 41 = 11. This expression uses each number exactly once and evaluates to the target number 11. </reasoning> <answer> \boxed{89 - 37 - 41}</answer> high confidence rapidly accumulates at the end of the se- quence. As diffusion ...

  12. [12]

    Input Projection:The hidden states from the diffusion backbone (D= 4096 ) are first projected down to the planner’s dimension (dmodel = 128)

  13. [13]

    Lightweight Positional Embedding:Positional em- beddings with a low dimension ( dpos = 16 ) are pro- jected to dmodel = 128 to be added to the input fea- tures then input to the transformer layer with ReLU activation in between

  14. [14]

    Final score for the sampled embeddings is obtained as an average of these values

    Scoring Head:The transformer outputs for each token are projected to a scalar value. Final score for the sampled embeddings is obtained as an average of these values. Training ConfigurationThe planner is trained using the Binary Cross Entropy loss. We employ the AdamW opti- mizer with a fixed learning rate of 1e-4 and a batch size of 256. To prevent overf...

    2025

  15. [15]

    Zero-Cost Annealing:The EOS temperature annealing requires only a simple scalar multiplication, adding no measurable delay. Training Compute OverheadOur method is excep- tionally lightweight, especially when contrasted with the massive memory and compute requirements of standard model alignment techniques in RLVR or standard RLHF paradigms (Ouyang et al.,...

    2022

  16. [16]

    Without the need for gradient computation or optimizer states for the large language model, the peak memory footprint is drastically reduced

    Offline Trajectory Generation (Inference-Only):Sam- pling training data requires an upfront compute invest- ment but is strictly a forward-pass operation on a frozen backbone. Without the need for gradient computation or optimizer states for the large language model, the peak memory footprint is drastically reduced. Moreover, this is a one-time, highly pa...

  17. [17]

    Planner Optimization (Lightweight Training):Since gradients are strictly confined to 5M-parameter planner, the training converges rapidly—taking approximately 5 minutes on a single A100 GPU—with a negligible memory footprint. By isolating the 8B model entirely to inference and restrict- ing backpropagation exclusively to the 5M planner module, our approac...