{
  "abstract": "Masked diffusions are popular generative models for discrete distributions. Unlike standard autoregressive sampling, they reveal several coordinates in parallel, approximating each block's joint conditional law by a product of one-coordinate conditionals. The resulting procedure, usually called tau-leaping, reduces computational cost but introduces a factorization error ($\\varepsilon_\\text{fact}$), even with perfectly learned predictors. We study the resulting tradeoff between generative accuracy and computational cost, focusing on how to choose a denoising schedule to minimize $\\varepsilon_\\text{fact}$ for a fixed sampling budget. To do so, we establish an exact integral representation of $\\varepsilon_\\text{fact}$ separating the schedule from the target's dependence structure, summarized by a dependence density $ρ$. This representation yields recursive stationarity equations for optimal schedules and allows us to quantify how estimation errors in $ρ$ affect schedule selection. As the dimension $N$ and sampling budget grow, we characterize the optimal schedule and quantify the cost of random block sizes relative to a deterministic planner. We highlight a fundamental dichotomy: if $ρ$ converges uniformly to a strictly positive continuous profile as $N\\to\\infty$, schedule optimization can only improve the leading constant of $\\varepsilon_\\text{fact}$, while if $ρ$ degenerates, schedule optimization can improve the asymptotic order. Examples based on stationary processes and exchangeable mixtures illustrate these regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21960",
  "author_total": 2,
  "authors": [
    {
      "name": "Cecilia Secchi"
    },
    {
      "name": "Giacomo Zanella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4cqr1c13rkc3y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21960",
  "fulltext_url": null,
  "id": "4cqr1c13rkc3y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21960",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7213937302",
  "pdf_url": "https://arxiv.org/pdf/2609.21960",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4cqr1c13rkc3y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2609.21960",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21960"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Schedule optimization for tau-leaping in masked discrete diffusion",
  "title_text": "Schedule optimization for tau-leaping in masked discrete diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/4cqr1c13rkc3y",
  "venue": "arXiv",
  "versions": []
}