{
  "abstract": "Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30539",
  "author_total": 5,
  "authors": [
    {
      "name": "Yi Zhang"
    },
    {
      "name": "Rui Guo"
    },
    {
      "name": "Mengchu Xu"
    },
    {
      "name": "Zhaofeng Liu"
    },
    {
      "name": "Yonina C. Eldar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ez3534b6499k5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30539",
  "fulltext_url": null,
  "id": "ez3534b6499k5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30539",
  "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",
      "eess.SP"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7214606346",
  "pdf_url": "https://arxiv.org/pdf/2609.30539",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ez3534b6499k5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:03Z",
      "native_id": "2609.30539",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30539"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding",
  "title_text": "Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:03Z",
  "url": "https://research.draconitic.com/paper/ez3534b6499k5",
  "venue": "arXiv",
  "versions": []
}