{"ID":6538263,"CreatedAt":"2026-07-14T02:54:43.516908796Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10951","arxiv_id":"2607.10951","title":"Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion","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.","short_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 j...","url_abs":"https://arxiv.org/abs/2607.10951","url_pdf":"https://arxiv.org/pdf/2607.10951v1","authors":"[\"Pascal Jutras-Dubé\",\"Patrick Pynadath\",\"Jeremy Lu\",\"Yuan Gao\",\"Ruqi Zhang\"]","published":"2026-07-12T23:03:32Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[\"Diffusion Model\"]","has_code":false}