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DeMTS: Denoising Trajectories as Multivariate Time Series for Hallucination Detection in Diffusion Language Models

The paper proposes DeMTS, a novel hallucination detection framework for Diffusion Large Language Models that treats denoising trajectories as multivariate time series to preserve complete token-step structural information, thereby outperforming existing methods by effectively capturing complex patterns like inconsistent convergence and cross-token fault propagation.

Original authors: Xin Zhang, Yili Wang, Yue Tan, Xin He, Yanyu Qian, Yixin Liu, Yi Chang, Shirui Pan, Xin Wang

Published 2026-08-18

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CC BY 4.0

Original authors: Xin Zhang, Yili Wang, Yue Tan, Xin He, Yanyu Qian, Yixin Liu, Yi Chang, Shirui Pan, Xin Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the rapidly evolving world of artificial intelligence, a new generation of text-generating machines has emerged, moving away from the traditional method of writing one word after another in a strict line. Instead, these models, known as diffusion large language models, generate text through a process of iterative refinement. Imagine a blurry image that slowly comes into focus; similarly, these models start with a jumbled, noisy sequence of words and gradually clean it up, step by step, until a coherent sentence emerges. While this approach offers unique advantages in speed and flexibility, it shares a critical flaw with its predecessors: the tendency to hallucinate. This is not a case of the machine dreaming, but rather a failure of fact-checking, where the model produces fluent, confident-sounding sentences that contain completely false or unsupported information. Detecting these errors is difficult because the final output often looks perfect, hiding the mistakes that occurred during the messy middle stages of creation.

Researchers have long tried to catch these errors by looking at the final answer or by checking how uncertain the model was at specific moments. However, a new study suggests that these methods often miss the most telling clues. The problem is that existing detection tools tend to flatten the complex history of how the model created the text. They either look only at the timeline of the creation process or only at the individual words, effectively discarding the rich, two-dimensional map of how uncertainty evolved across both time and the specific words being formed. By compressing this data, they lose the ability to see how a mistake in one part of the sentence might ripple through to corrupt the rest, or how different words might fail to settle on a confident truth at the same time.

To solve this, a team of scientists has developed a new framework called DeMTS, which treats the entire creation process of a sentence as a complex, multi-layered signal rather than a simple list of steps. Instead of forcing the model's internal signals into a single line, the researchers organized the data to preserve the relationship between every word and every moment of the creation process. They realized that the raw positions of words in a sentence are not stable enough to track reliably, as the same position might hold different meanings in different sentences. To fix this, they created a system that groups the noisy, shifting signals from the model into stable, consistent categories. Think of it like sorting a chaotic pile of mixed-up puzzle pieces into distinct, labeled boxes based on their shape and color, rather than trying to track them by their original, confusing order.

Once these stable groups were formed, the researchers applied a dynamic modeling technique to watch how these groups interacted and changed over time. They found that hallucinations leave a distinct fingerprint in this process. In a truthful response, the various parts of the sentence tend to settle into a confident state together. In a hallucinated response, however, the model often shows signs of "inconsistent convergence," where some words become highly confident while others remain shaky and uncertain. Furthermore, they observed "cross-token fault propagation," where an unstable or incorrect word causes neighboring words to drift away from the truth, creating a chain reaction of error that spreads through the sentence. By tracking these specific patterns of instability and interaction, the new system can spot a lie before it is even fully spoken.

The researchers tested this approach on two different large language models across three distinct question-answering datasets, ranging from general knowledge to complex reasoning tasks. The results showed that this new method significantly outperformed existing techniques, successfully identifying false information with much higher accuracy. Crucially, the system remained efficient and robust, proving that it could generalize its findings to new types of questions without needing to be retrained for every specific topic. The study demonstrates that by respecting the full, two-dimensional structure of how these models think—keeping the timeline and the word relationships intact—we can build much better safeguards against the subtle, confident errors that plague modern artificial intelligence.

Technical Summary: DeMTS for Hallucination Detection in Diffusion Language Models

Problem Statement

Diffusion Large Language Models (D-LLMs) have emerged as a promising alternative to autoregressive models, generating text through iterative denoising rather than strict left-to-right decoding. However, like their autoregressive counterparts, D-LLMs are susceptible to hallucinations—generating fluent but factually incorrect or unsupported content.

Existing hallucination detection methods for D-LLMs primarily rely on uncertainty trajectories from the denoising process. However, current approaches typically compress these trajectories along a single dimension: either selecting specific informative steps (temporal compression) or identifying specific indicative tokens (token compression). This unidimensional compression overlooks the rich, two-dimensional structure of the denoising process, where token-level uncertainty evolves across diffusion steps. Consequently, these methods fail to capture critical hallucination patterns, such as:

Inconsistent Convergence: In hallucinated responses, different tokens may converge to markedly different confidence levels during late denoising stages, revealing abnormal inter-token relations.
Cross-Token Fault Propagation: An unstable or incorrect token state can propagate errors to contextually connected tokens, causing their entropy trajectories to deviate jointly from a factual path.

The core challenge is how to explicitly model these token-step uncertainty trajectories to capture both cross-token dependencies and temporal dynamics without losing the structural information inherent in the two-dimensional token-step matrix.

Methodology: DeMTS

The authors propose DeMTS (Denoising Trajectories as Multivariate Time Series), a framework that treats D-LLM denoising trajectories as multivariate time series over learnable latent variables. The framework addresses two primary challenges: (1) constructing stable variables from semantically unstable token positions, and (2) modeling relational temporal dynamics.

1. Trajectory-Preserving Token-to-Variable (T2V) Assignment

Since raw token positions lack consistent semantic identities across samples and during the denoising process, DeMTS introduces a T2V module to map token signals into stable latent variables.

Schedule-Aware Uncertainty Normalization: To mitigate global uncertainty biases induced by the denoising schedule (where early steps are noisier), token uncertainties are normalized within each step based on mean and variance.
Variable Axis Construction: The module constructs a latent variable axis by assigning token signals to $K$ $K$ latent variables based on a combination of:
- Uncertainty Dynamics: Normalized entropy states.
- Contextual Semantics: Token embeddings from the D-LLM.
- Positional Structure: Multi-frequency Fourier representations to capture both global ordering and local neighborhood relations.
  A content-adaptive gate regulates the contribution of structural information based on the current token state.
Trajectory-Preservation Constraint: To prevent the aggregation process from smoothing out critical local denoising dynamics, DeMTS imposes a constraint that ensures the reconstructed variations in the latent space match the original token-level variations in both magnitude (Amplitude Preservation Loss) and temporal direction (Direction Consistency Loss).

2. Dynamic Multivariate Temporal Modeling (DMTM)

Once the trajectory is transformed into a sequence of latent variables, DeMTS models their evolution and interactions.

Stage-Adaptive Inter-Variable Interaction: Dependencies among latent variables evolve as denoising progresses. Early steps are noisy, while later steps are more stable. DeMTS employs a trajectory-reliability gate that limits information fusion in noisy early stages and progressively strengthens interactions among stabilized variables in later stages. This is achieved via attention-based interaction weighted by a reliability factor $\rho = (T-t)/T$ .
Variable-Wise Temporal Dynamics Modeling: After integrating relational evidence, the framework models the temporal evolution of each latent variable using temporal self-attention, capturing how the dependency-enhanced state changes over the denoising steps.
Prediction: The final multivariate temporal representation is fed into a lightweight classifier to predict the hallucination probability.

Key Contributions

Formulation: The paper formulates D-LLM hallucination detection as a multivariate time series learning problem, identifying that existing methods fail to preserve the two-dimensional token-step structure.
Framework: DeMTS introduces a novel architecture that transforms semantically unstable token signals into stable latent variables (via T2V) and jointly captures dynamic inter-variable dependencies and variable-wise temporal evolution (via DMTM).
Performance: Extensive experiments demonstrate that DeMTS outperforms existing baselines while maintaining robustness, efficiency, and cross-task transferability.

Experimental Results

The authors evaluated DeMTS on two D-LLM backbones (LLaDA-8B-Instruct and Dream-7B-Instruct) across three benchmarks (TriviaQA, HotpotQA, and CommonsenseQA) with generation lengths of 64 and 128 steps.

Performance: DeMTS achieved the highest AUROC scores across all settings. For instance, on LLaDA-8B-Instruct with 64 steps, DeMTS scored 89.8% on TriviaQA, outperforming the previous state-of-the-art trajectory-based method (DynHD, 86.1%) and latent-based methods (EigenScore, 66.9%).
Comparison:
- vs. Output-based methods: DeMTS significantly outperformed methods relying solely on final output statistics (e.g., Perplexity, Semantic Entropy), confirming that output-level evidence is insufficient for detecting hallucinations formed during iterative denoising.
- vs. Latent-based methods: DeMTS surpassed methods using static internal representations, highlighting the necessity of modeling evolving temporal dependencies.
- vs. Other Trajectory-based methods: DeMTS outperformed TraceDet and DynHD, validating the benefit of preserving the full multivariate structure rather than compressing trajectories.
Ablation Studies: Removing any component (e.g., T2V, DMTM, or preservation losses) consistently degraded performance. Specifically, using raw token positions as variables caused the most significant drop, confirming the need for stable latent variable construction.
Generalization & Efficiency: DeMTS demonstrated strong zero-shot cross-task generalization (training on one dataset, testing on others) and achieved the best trade-off between AUROC and inference time, being faster than many baselines due to operating in a compact latent space ( $K \ll N$ ).

Significance and Claims

The paper claims that DeMTS bridges a critical gap in D-LLM hallucination detection by explicitly modeling the two-dimensional token-step uncertainty structure. By treating denoising trajectories as multivariate time series, the framework captures complex patterns like inconsistent convergence and cross-token fault propagation that unidimensional compression methods miss.

The authors emphasize that their approach does not require repeated generation or additional forward passes through the D-LLM backbone, making it computationally efficient. They position DeMTS as a robust, transferable, and effective solution for detecting hallucinations in the emerging paradigm of diffusion-based text generation, offering a new perspective on leveraging process-level evidence for reliability assessment.