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Path-Dependent Denoising: A Non-Conservative Field Perspe...
Jeonseong Ki · 2026-05-12 · via cs.LG updates on arXiv.org

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Abstract:Diffusion language models (DLMs) offer a structural alternative to autoregressive generation: denoising can update tokens in arbitrary orders or in parallel rather than along a fixed left-to-right chain. In practice, fast DLM decoding remains strongly order-sensitive and often drifts toward autoregressive-like trajectories. We trace this tension to compatibility. At each reverse-time step, a DLM provides local denoising conditionals over the unresolved tokens. Arbitrary-order denoising becomes well defined when these local conditionals compose into order-invariant pseudo-joints.
We formalize this view by defining order-induced pseudo-joints and a local denoising circulation: the log-ratio between the two pseudo-joints obtained by swapping a pair of unresolved positions. This circulation is zero under compatible conditionals, and global order gaps decompose into sums of local circulations along adjacent swaps. We further separate incompatibility-driven path dependence from conditional-dependence error in parallel updates and from order-specific estimation error. The resulting framework provides inference-only diagnostics for testing when DLM decoding is genuinely order-free.
Subjects: Machine Learning (cs.LG)
Cite as: arXiv:2605.09303 [cs.LG]
  (or arXiv:2605.09303v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2605.09303

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Jeonseong Kim [view email]
[v1] Sun, 10 May 2026 04:00:52 UTC (17 KB)