arxiv: 2605.14570 · v1 · submitted 2026-05-14 · 💻 cs.CL

Recognition: 2 theorem links

· Lean Theorem

Uncertainty Quantification for Large Language Diffusion Models

Artem Vazhentsev , Vladislav Smirnov , David Li , Maxim Panov , Timothy Baldwin , Artem Shelmanov

Authors on Pith no claims yet

Pith reviewed 2026-05-15 01:33 UTC · model grok-4.3

classification 💻 cs.CL

keywords uncertainty quantificationlarge language diffusion modelshallucination detectiondenoising trajectorymasked diffusiontrajectory dissimilarityzero-shot UQ

0 comments

The pith

Expected trajectory dissimilarity from the denoising process lower-bounds the masked diffusion training objective and serves as a lightweight uncertainty score for large language diffusion models.

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

The paper shows that large language diffusion models can detect their own hallucinations using signals extracted directly from the single denoising trajectory instead of repeated sampling. Intermediate token generations, remasking patterns, and a measure of trajectory dissimilarity supply these signals at negligible extra cost. A proof establishes that the expected dissimilarity lower-bounds the masked diffusion training objective, giving theoretical grounding for its use as an uncertainty indicator. Experiments across three tasks and eight datasets demonstrate that the resulting scores approach the accuracy of expensive sampling baselines while cutting computation by up to two orders of magnitude. This combination preserves the inference speed advantage of diffusion models while adding reliable hallucination detection.

Core claim

We prove that expected trajectory dissimilarity lower bounds the masked diffusion training objective, which motivates its usage as an uncertainty score. By combining masked diffusion likelihoods with trajectory-based semantic dissimilarity we obtain lightweight zero-shot signals from intermediate generations, token remasking dynamics, and denoising complexity that achieve strong cost-performance trade-offs on multiple tasks and models.

What carries the argument

Expected trajectory dissimilarity along the denoising path, which lower-bounds the masked diffusion training objective and functions as a zero-shot uncertainty score when combined with diffusion likelihoods.

If this is right

Uncertainty scores become available in a single denoising pass rather than multiple independent generations.
Hallucination detection approaches the performance of sampling-based methods at up to 100x lower compute.
Large language diffusion models can be deployed with both faster inference and built-in reliability checks.
The same trajectory signals apply across generation, classification, and other sequence tasks.

Where Pith is reading between the lines

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

The lower-bound relation might allow uncertainty signals to be folded back into the training objective itself for more robust models.
Similar trajectory-based measures could be tested on image or audio diffusion models to check for broader applicability.
If the correlation holds, these scores could be used to trigger selective abstention or human review in real-time applications.

Load-bearing premise

Signals extracted from the denoising trajectory correlate with actual hallucination risk on the tasks and models tested.

What would settle it

A dataset or model where expected trajectory dissimilarity shows near-zero correlation with human-judged hallucination rates while sampling-based baselines remain predictive would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.14570 by Artem Shelmanov, Artem Vazhentsev, David Li, Maxim Panov, Timothy Baldwin, Vladislav Smirnov.

**Figure 2.** Figure 2: UQ performance (PRR↑) versus computational overhead (runtime in seconds↓) averaged across all datasets. based statistics, provide very low-cost uncertainty estimates but are less accurate and generally insufficient for high-quality UQ. Our proposed methods, D-CoCoA-G and D-CoCoA-L, consistently achieve a strong balance between performance and efficiency. They clearly outperform other low- to medium-compl… view at source ↗

**Figure 3.** Figure 3: Comparison of uncertainty quantification performance (PRR [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗

**Figure 4.** Figure 4: Comparison of uncertainty quantification performance (PRR [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗

**Figure 5.** Figure 5: Comparison of uncertainty quantification performance (ROC-AUC [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗

**Figure 6.** Figure 6: Comparison of uncertainty quantification performance (ROC-AUC [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗

**Figure 7.** Figure 7: Comparison of uncertainty quantification performance (ROC-AUC [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗

read the original abstract

Large Language Diffusion Models (LLDMs) are emerging as an alternative to autoregressive models, offering faster inference through higher parallelism. Similar to autoregressive LLMs, they remain prone to hallucinations, making reliable uncertainty quantification (UQ) crucial for safe deployment. However, existing UQ methods are fundamentally misaligned with this new paradigm: they assume autoregressive factorization or use expensive repeated sampling, negating the efficiency of LLDMs. In this work, we present the first systematic study of UQ for LLDMs and propose lightweight, zero-shot uncertainty signals derived from the iterative denoising process, leveraging intermediate generations, token remasking dynamics, and denoising complexity. We further adapt a state-of-the-art UQ method to LLDMs by combining masked diffusion likelihoods with trajectory-based semantic dissimilarity. We prove that expected trajectory dissimilarity lower bounds the masked diffusion training objective, which motivates its usage as an uncertainty score. Comprehensive experiments across three tasks, eight datasets, and two models show that our method achieves a great cost-performance trade-off: it approaches the strongest sampling-based baselines while incurring up to 100x lower computational overhead. Our work demonstrates that LLDMs can deliver both fast inference and reliable hallucination detection simultaneously.

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.

Desk Editor's Note private letter to a colleague

This is the first systematic UQ study for LLDMs, with new denoising signals and a clean lower-bound proof, but the proof does not yet tightly connect to hallucination detection.

read the letter

The main thing to know is that Vazhentsev et al. have done the first dedicated exploration of uncertainty quantification for large language diffusion models. They pull zero-shot signals straight from the denoising process—intermediate generations, remasking dynamics, and a trajectory dissimilarity measure—and they adapt an existing UQ approach by combining masked diffusion likelihoods with that dissimilarity term. The proof that expected trajectory dissimilarity lower-bounds the training objective is a solid theoretical move and gives a direct reason to treat the dissimilarity score as an uncertainty signal. Their experiments run across three tasks, eight datasets, and two models, and they show the method gets close to strong sampling baselines at up to 100x lower cost. That efficiency result is the clearest practical win, since it keeps the speed advantage that makes LLDMs interesting in the first place. The softer spot is the step from the training objective to actual hallucination risk. The objective measures expected denoising error, so the lower bound holds mathematically, but it still needs the assumption that higher dissimilarity reliably flags semantic mistakes rather than just reconstruction noise. An ablation that isolates the dissimilarity term against plain denoising loss would have strengthened the empirical link. The abstract reports broad coverage, yet without error bars or full split details it is hard to judge how stable the gains are. This paper is for groups working on non-autoregressive generation or cheap safety checks for LLMs. It deserves a serious referee because it opens the problem and supplies both theory and concrete numbers, even if the theory-to-hallucination bridge could be tested more directly.

Referee Report

1 major / 2 minor

Summary. The paper presents the first systematic study of uncertainty quantification (UQ) for Large Language Diffusion Models (LLDMs). It proposes lightweight zero-shot signals derived from the iterative denoising process (intermediate generations, token remasking dynamics, and denoising complexity), adapts a state-of-the-art UQ method by combining masked diffusion likelihoods with trajectory-based semantic dissimilarity, and proves that expected trajectory dissimilarity lower-bounds the masked diffusion training objective. Experiments across three tasks, eight datasets, and two models demonstrate that the proposed methods achieve competitive hallucination detection performance relative to sampling-based baselines while incurring up to 100x lower computational overhead.

Significance. If the central theoretical link and empirical results hold, the work is significant because it aligns UQ methods with the parallel inference advantages of LLDMs rather than forcing autoregressive assumptions or expensive sampling. The proof supplies an independent mathematical grounding for the dissimilarity score, and the scale of the evaluation (eight datasets, multiple tasks and models) provides a reproducible basis for the claimed cost-performance trade-off.

major comments (1)

[§4] §4 (theoretical motivation and proof): The inequality showing that expected trajectory dissimilarity lower-bounds the masked diffusion objective is mathematically independent, yet the manuscript does not demonstrate via ablation that the dissimilarity term supplies predictive power for hallucination risk beyond the scalar denoising loss alone. Because the training objective quantifies expected denoising error under the forward process, an additional assumption is required that trajectory dissimilarity reliably tracks semantic hallucination rather than low-loss but factually incorrect outputs; this assumption is load-bearing for the UQ claim but is not directly tested.

minor comments (2)

[Experiments] Experiments section: error bars, confidence intervals, and explicit data-exclusion criteria for the eight datasets are not reported, which limits verification of the claimed performance margins.
[Notation] Notation: the precise definition of 'trajectory dissimilarity' (e.g., the distance metric over intermediate generations) should be given its own numbered equation for clarity when referenced in the proof and experiments.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and for recognizing the potential significance of our work on uncertainty quantification for Large Language Diffusion Models. We address the major comment below and plan to incorporate revisions to strengthen the manuscript.

read point-by-point responses

Referee: [§4] §4 (theoretical motivation and proof): The inequality showing that expected trajectory dissimilarity lower-bounds the masked diffusion objective is mathematically independent, yet the manuscript does not demonstrate via ablation that the dissimilarity term supplies predictive power for hallucination risk beyond the scalar denoising loss alone. Because the training objective quantifies expected denoising error under the forward process, an additional assumption is required that trajectory dissimilarity reliably tracks semantic hallucination rather than low-loss but factually incorrect outputs; this assumption is load-bearing for the UQ claim but is not directly tested.

Authors: We thank the referee for highlighting this important point. The proof establishes that the expected trajectory dissimilarity lower-bounds the masked diffusion training objective, providing theoretical motivation for using dissimilarity as part of the uncertainty signal. However, we acknowledge that the current manuscript does not include an explicit ablation study isolating the contribution of the dissimilarity term beyond the scalar denoising loss. Our experiments demonstrate the effectiveness of the combined approach (likelihoods + dissimilarity) in achieving near sampling-based performance at much lower cost, but a direct comparison to denoising loss alone is indeed missing. In the revised manuscript, we will add such an ablation across the eight datasets to quantify the additional predictive power. Regarding the assumption that dissimilarity tracks semantic hallucination, the empirical results on hallucination detection tasks support this, as the method outperforms or matches baselines. We will also add a discussion on potential limitations, including cases where low-loss but incorrect outputs might occur, to address this concern. revision: yes

Circularity Check

0 steps flagged

No circularity: mathematical bound provides independent grounding for uncertainty score

full rationale

The paper's central derivation is a proof that expected trajectory dissimilarity lower-bounds the masked diffusion training objective. This is presented as a direct mathematical result motivating the uncertainty score, without reducing to fitted parameters, self-definitional loops, or load-bearing self-citations. Experiments across tasks and datasets provide separate empirical validation. No steps in the provided abstract or claims exhibit the enumerated circular patterns; the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the iterative denoising process in masked diffusion models and the mathematical relationship between trajectory dissimilarity and the training objective; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption LLDMs follow an iterative masked diffusion denoising process whose intermediate states can be observed and compared
Invoked when defining the uncertainty signals from intermediate generations and trajectory dissimilarity.

pith-pipeline@v0.9.0 · 5523 in / 1219 out tokens · 47443 ms · 2026-05-15T01:33:30.058730+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages · 1 internal anchor

[1]

Association for Computational Linguistics. K. Cobbe, V . Kosaraju, M. Bavarian, M. Chen, H. Jun, L. Kaiser, M. Plappert, J. Tworek, J. Hilton, R. Nakano, C. Hesse, and J. Schulman. Training veriﬁers to solve math word problems. CoRR, abs/2110.14168, 2021. J. Duan, H. Cheng, S. Wang, A. Zavalny, C. Wang, R. Xu, B. Kailkhura, and K. Xu. Shifting atten- tion...

work page internal anchor Pith review Pith/arXiv arXiv 2021
[2]

Guidelines: • The answer [N/A] means that the abstract and introduction do not include the claims made in the paper

Claims Question: Do the main claims made in the abstract and introduction accurately reﬂect the paper’s contributions and scope? Answer: [Y es] Justiﬁcation: Y es, the claims made in the abstract and introduction are precisely supported by the description of the method in Section 3 and by the experimental evaluations in Sec- tion 4. Guidelines: • The answ...

work page
[3]

Limitations

Limitations Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Y es] Justiﬁcation: Y es, the limitations of the work are discussed in Appendix E. Guidelines: • The answer [N/A] means that the paper has no limitation while the answer [No] means that the paper has limitations, but those are not discussed in the p...

work page
[4]

Guidelines: • The answer [N/A] means that the paper does not include theoretical results

Theory assumptions and proofs Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof? 27 Answer: [Y es] Justiﬁcation: Y es, the paper provides theoretical results in Theorem 1, with the full set of assumptions in Section 3.3 and complete proof in Appendix A. Guidelines: • The answer [N/...

work page
[5]

Guidelines: • The answer [N/A] means that the paper does not include experiments

Experimental result reproducibility Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclu- sions of the paper (regardless of whether the code and data are provided or not)? Answer: [Y es] Justiﬁcation: All necessary details for ...

work page
[6]

Guidelines: • The answer [N/A] means that paper does not include experiments requiring code

Open access to data and code Question: Does the paper provide open access to the data and code, with sufﬁcient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Y es] Justiﬁcation: The implementation code will be anonymously included in the supplementary materials to ensure transparency a...

work page
[7]

No model training is performed in this work

Experimental setting/details Question: Does the paper specify all the training and test details (e.g., data splits, hyperpa- rameters, how they were chosen, type of optimizer) necessary to understand the results? Answer: [Y es] Justiﬁcation: All relevant details of the testing experiments are provided in Section 4 and Appendix D. No model training is perf...

work page
[8]

To further demonstrate the robustness of our ﬁndings, we conducted experiments across two LLMs and eight datasets from diverse domains and tasks

Experiment statistical signiﬁcance Question: Does the paper report error bars suitably and correctly deﬁned or other appropri- ate information about the statistical signiﬁcance of the experiments? Answer: [Y es] Justiﬁcation: Reliability of the results is ensured by ﬁxing random seeds and using greedy decoding, which leads to deterministic generation. To ...

work page
[9]

Guidelines: • The answer [N/A] means that the paper does not include experiments

Experiments compute resources Question: For each experiment, does the paper provide sufﬁcient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [Y es] Justiﬁcation: Details about resources and implementation are provided in Appendix D.1. Guidelines: • The answer [N/A] ...

work page
[10]

Guidelines: • The answer [N/A] means that the authors have not reviewed the NeurIPS Code of Ethics

Code of ethics Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines? Answer: [Y es] Justiﬁcation: Y es, the research conducted in this paper conforms in every respect with the NeurIPS Code of Ethics. Guidelines: • The answer [N/A] means that the authors hav...

work page
[11]

30 Guidelines: • The answer [N/A] means that there is no societal impact of the work performed

Broader impacts Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed? Answer: [Y es] Justiﬁcation: The broader impact of our work is discussed in Appendix F. 30 Guidelines: • The answer [N/A] means that there is no societal impact of the work performed. • If the authors answer [N/A] ...

work page
[12]

No new models or datasets are released as part of this work

Safeguards Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pre-trained language models, image generators, or scraped datasets)? Answer: [Y es] Justiﬁcation: Our work focuses on hallucination detection in LLMs, which does not intro- duce new safety ri...

work page
[13]

Guidelines: • The answer [N/A] means that the paper does not use existing assets

Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected? Answer: [Y es] Justiﬁcation: Y es, we appropriately credit the authors and licenses for all models, methods, and datasets uti...

work page
[14]

Guidelines: • The answer [N/A] means that the paper does not release new assets

New assets Question: Are new assets introduced in the paper well documented and is the documenta- tion provided alongside the assets? Answer: [N/A] Justiﬁcation: The paper does not release new datasets or models. Guidelines: • The answer [N/A] means that the paper does not release new assets. • Researchers should communicate the details of the dataset/cod...

work page
[15]

Guidelines: • The answer [N/A] means that the paper does not involve crowdsourcing nor research with human subjects

Crowdsourcing and research with human subjects Question: For crowdsourcing experiments and research with human subjects, does the pa- per include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)? Answer: [N/A] Justiﬁcation: This work does not involve crowdsourcing or researc...

work page
[16]

Guidelines: 32 • The answer [N/A] means that the paper does not involve crowdsourcing nor research with human subjects

Institutional review board (IRB) approvals or equivalent for research with human subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or ...

work page
[17]

Declaration of LLM usage Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientiﬁc rigor, or originality of the research, declaration i...

work page