{
  "abstract": "Discrete diffusion models have become a powerful framework for modeling complex discrete distributions across a range of applications. While theoretical convergence guarantees depend on consistency between the target and training distributions, such a case rarely holds in practice, making score mismatch a central challenge in discrete diffusion sampling. This is particularly relevant to zero-shot conditional generation, where a model trained on the unconditional distribution is directly reused at inference time to sample from a conditional target distribution. In this paper, we provide the first theoretical analysis for score-mismatched discrete diffusion models and derive a general KL divergence upper bound that clearly identifies the additional bias caused by such a mismatch. Our analysis covers partial-observation constraints, including text infilling, sentence completion, and more general coordinatewise set constraints. Specifically, we analyze the classical Conditional SEDD sampler and show that it can incur a bias term that scales with the dimension, vocabulary size, and compatibility. Based on this analysis, we propose a Randomized Hard Clamping (RHC) sampler for coordinatewise set constraints. We show that the assignment probabilities can be expressed exactly by the unconditional scores with absorbing rate. Finally, numerical and real-data experiments demonstrate the effectiveness of the proposed RHC sampler.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21061",
  "author_total": 5,
  "authors": [
    {
      "name": "Renxiang Huang"
    },
    {
      "name": "Yuchen Liang"
    },
    {
      "name": "Yingbin Liang"
    },
    {
      "name": "Ness Shroff"
    },
    {
      "name": "Lifeng Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx7f3pj8jkg6z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21061",
  "fulltext_url": null,
  "id": "fx7f3pj8jkg6z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21061",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7222523950",
  "pdf_url": "https://arxiv.org/pdf/2610.21061",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx7f3pj8jkg6z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:00Z",
      "native_id": "2610.21061",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21061"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Score Mismatch and Set-Constrained Sampling in Zero-Shot Conditional Discrete Diffusion",
  "title_text": "Score Mismatch and Set-Constrained Sampling in Zero-Shot Conditional Discrete Diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/fx7f3pj8jkg6z",
  "venue": "arXiv",
  "versions": []
}