Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion

• URL: http://arxiv.org/abs/2607.10951v1
• Date: Sun, 12 Jul 2026 23:03:32 GMT
• Title: Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion
• Abstract summary: We introduce Sticky Jump Diffusions (SJDs) on $mathbb Rd$ whose discrete anchors are token embeddings.<n>In forward time, anchors release their mass at a hazard rate and the released mass diffuses in the continuous ambient space.<n>Time reversal couples a score-driven SDE with a sticky jump kernel whose rate and destination are fixed by flux balance with the forward law.
• Score: 23.795460583709907
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce Sticky Jump Diffusions (SJDs), continuous-time Markov processes on $\mathbb R^d$ whose discrete anchors are token embeddings. In forward time, anchors release their mass at a hazard rate and the released mass diffuses in the continuous ambient space; time reversal couples a score-driven SDE with a sticky jump kernel whose rate and destination are fixed by flux balance with the forward law. We estimate the score and the per-anchor reverse hazards from a single denoising classifier via Denoising Hazard Matching, the hazard analogue of denoising score matching, with simulation-free cross-entropy training. SJD recovers masked diffusion, continuous diffusion, and hybrid diffusion as limits. Its reversal explains features that each family treats as given: the mask of masked diffusion carries no evidence about the source token because the unsticking kernel of every anchor collapses to the same absorbing point; the terminal projection of continuous diffusion is required due to the absence of atoms in its forward marginal, without which flux balance yields no reverse jumps; and the update rules of hybrid diffusion (commit rate, destination, and drift) all follow from flux balance rather than from separate design. Beyond these limits, the unsticking kernel becomes a design space: a cross-position blending corrupts each position toward a blend of its neighbors' clean values or embeddings, turning dependency structure such as spatial locality or a constraint graph into an inductive bias of the corruption itself, and improves over the identity-kernel hybrid on CIFAR-10, Text8, and Sudoku.

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