Temporally-Resolved Token Attribution Reveals the Generation Dynamics of Diffusion Language Models

cs.CL cs.AI cs.LG Darpan Aswal, C\'eline Hudelot · Oct 1, 2026
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What it does
Diffusion language models generate text through iterative denoising rather than left-to-right prediction, making attribution a spatiotemporal problem: support for any output token is distributed across both network depth and timesteps....
Why it matters
This paper introduces Diffusion Layer Integrated Gradients (DLIG), which extends Integrated Gradients to score a DLM's commitment to its completion at any chosen layer and denoising step, decomposing it into per-token contributions. It...
Main concern
The paper presents a technically sound adaptation of IG to the DLM setting. By proving that at any fixed (layer, step) pair DLIG reduces exactly to standard IG applied to the upstream function $G_t^{(\ell)}$, the authors rigorously...
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Plain-language introduction

Diffusion language models generate text through iterative denoising rather than left-to-right prediction, making attribution a spatiotemporal problem: support for any output token is distributed across both network depth and timesteps. This paper introduces Diffusion Layer Integrated Gradients (DLIG), which extends Integrated Gradients to score a DLM's commitment to its completion at any chosen layer and denoising step, decomposing it into per-token contributions. It matters because existing token-attribution tools ignore the denoising trajectory entirely, while interventional alternatives are computationally expensive.

Critical review
Verdict
Bottom line

The paper presents a technically sound adaptation of IG to the DLM setting. By proving that at any fixed (layer, step) pair DLIG reduces exactly to standard IG applied to the upstream function $G_t^{(\ell)}$, the authors rigorously transfer completeness, implementation invariance, linearity, and symmetry-preservation guarantees (Section 3: "DLIG is exactly IG applied to the function $G_t^{(\ell)}$ with input $a=h^{(\ell)}_{t}(X_{t},C)$ and baseline $a'=h^{(\ell)}_{t}(X_{t},\varnothing)$"). The three demonstrations—ruling out depth-based explanations for a Yes bias in WiC, localizing reasoning chains even in ProsQA failures, and revealing late-emerging context reliance in infilling—convincingly illustrate DLIG's utility. However, the study is limited to a single 355M-parameter masked-diffusion model and no causal validation, as the authors acknowledge: "DLIG is a post-hoc gradient attribution method: it identifies where and when a model's committed output is gradient-sensitive to the prompt, not the causal circuit producing it, so its outputs are hypotheses to be confirmed, not mechanism at face value" (Section 9).

“DLIG is exactly IG applied to the function G_t^{(\ell)} with input a=h^{(\ell)}_{t}(X_{t},C) and baseline a'=h^{(\ell)}_{t}(X_{t},\varnothing):”
Aswal & Hudelot, DLIG paper · Section 3
“DLIG is a post-hoc gradient attribution method: it identifies where and when a model's committed output is gradient-sensitive to the prompt, not the causal circuit producing it, so its outputs are hypotheses to be confirmed, not mechanism at face value”
Aswal & Hudelot, DLIG paper · Section 9
What holds up

The axiomatic grounding is the strongest element. By instantiating the scalar map as $G_t^{(\ell)}$, the authors show that DLIG inherits IG's completeness, implementation invariance, linearity, and symmetry preservation exactly (Section 3.1). The empirical verification is equally careful: completeness is checked with hook-transparency, convergence from $m=200$ to $m=1000$, and a bit-exact partial-forward spot check across the full layer-and-step grid (Appendix A.1). The ProsQA analysis is particularly compelling—"Gold-path precision is nearly identical for successes and fails and carries no signal in a joint logistic model" (Section 6)—demonstrating that attribution localization survives even when the final answer is wrong, a genuinely surprising finding that distinguishes reading the right facts from executing the reasoning correctly.

“Gold-path precision is nearly identical for successes and fails and carries no signal in a joint logistic model”
Aswal & Hudelot, DLIG paper · Section 6
“endpoint scores recovered through the hook match the plain forward pass to floating-point precision at every grid cell”
Aswal & Hudelot, DLIG paper · Appendix A.1
Main concerns

The paper relies entirely on a single fine-tuned DiffuGPT-M (355M) checkpoint for all tasks, leaving open whether the dynamics generalize to larger, natively-trained DLMs or continuous-space and hybrid families. The underlying model's task performance is modest—WiC 63.6% overall with severe Yes-bias (90.8% same-sense vs. 36.4% different-sense), ProsQA 55.0% success, and ROCStories ROUGE-1 12.02 (Appendix A.2, Table 1)—so the interpretability findings describe a relatively weak system. Additionally, the self-generated scoring framing introduces circularity: the attribution target is the model's own emerging completion, and 22.3% of WiC steps carry zero attributable mass because no output has been committed yet (Appendix B, Table 7), making early-step dynamics unstable. While the authors frame DLIG as a hypothesis-generation tool, the absence of any causal validation—e.g., activation patching on highly attributed tokens—means the "mechanistic hypotheses" remain unverified.

“Overall accuracy 63.6%; Same-sense (Yes) accuracy 90.8%; Different-sense (No) accuracy 36.4%; ProsQA Success 55.0%; Infill ROUGE-1 12.02”
Aswal & Hudelot, DLIG paper · Appendix A.2, Table 1
“Aggregate over all 32 steps: 22.3%”
Aswal & Hudelot, DLIG paper · Appendix B, Table 7
Evidence and comparison

The evidence supports the narrower claim that DLIG produces coherent, complete attributions and generates non-obvious hypotheses. The comparison to Nguyen's attribution-contract taxonomy and Yao et al.'s temporal causal tracing (Section 2) fairly positions DLIG as a lightweight complement to expensive interventional analyses. However, the paper does not benchmark DLIG against simpler baselines such as layer-wise attention rollout or gradient norms, so readers cannot gauge whether the computational cost of step-wise IG integration is empirically justified relative to cheaper heuristics. The fixed-target versus self-generated analysis in Appendix A.4.1 is commendably candid, noting that "on high-ROUGE stories the fixed gold target lies close to the model's actual trajectory and receives elevated gradient signal for that reason alone, independent of how much the model relied on context," which means framing choices can inflate apparent correlations.

“on high-ROUGE stories the fixed gold target lies close to the model's actual trajectory and receives elevated gradient signal for that reason alone, independent of how much the model relied on context”
Aswal & Hudelot, DLIG paper · Appendix A.4.1
Reproducibility

The authors release code and model checkpoints, and hyperparameters, training splits, and prompt templates are documented in Appendix C. The main analysis uses $T=64$ denoising steps with $m=12$ Riemann points, and completeness is checked at finer resolutions (Appendix A.1). Reproduction is tractable with the DiffuGPT-M checkpoint. Blockers include the undisclosed random seed for the WiC/ProsQA test splits carved from public training data, and the ProsQA parsing pipeline that matches model generations to graph facts via fuzzy string matching involving manual templates (Appendix A.3). The implementation checks—confirming that "endpoint scores recovered through the hook match the plain forward pass to floating-point precision at every grid cell" and exact partial-forward agreement—go a long way toward ensuring correctness (Appendix A.1).

“endpoint scores recovered through the hook match the plain forward pass to floating-point precision at every grid cell”
Aswal & Hudelot, DLIG paper · Appendix A.1
“All three tasks finetune DiffuGPT-M, a masked-diffusion adaptation of GPT-2-medium (\sim 355M params)”
Aswal & Hudelot, DLIG paper · Appendix C
Abstract

This work presents Diffusion Layer Integrated Gradients (DLIG), a token attribution method for diffusion language models (DLMs) that extends Integrated Gradients (IG~\cite{sundararajan2017axiomatic}) to arbitrary layers and denoising steps. DLIG attributes a DLM's progressive commitment to a self-generated or fixed completion for an input prompt. We establish direct correspondences between DLIG and the IG axioms of completeness, implementation invariance, linearity, and symmetry preservation. As a lightweight complement to interventional analysis, DLIG provides an inexpensive first check of mechanistic hypotheses across the denoising trajectory. We demonstrate this on word-sense disambiguation, multi-hop graph reasoning, and sentence infilling, revealing how DLMs draw on inputs across positions, layers, and denoising steps.

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