{
  "abstract": "Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduce Flow Annealing Posterior Sampling (FLAPS), to our knowledge the first function-space posterior sampling framework that unifies stochastic-process regression and PDE inverse problems. Built on pretrained function-space flow-matching priors, FLAPS enables likelihood-guided posterior inference from sparse and noisy observations, supports variable query discretizations, and avoids explicit prior-density evaluation. Its Langevin correction uses a low-rank covariance preconditioner to exploit dominant function-space correlations across discretizations. Across Gaussian and non-Gaussian stochastic-process regression benchmarks and diverse PDE inverse problems, FLAPS produces coherent posterior samples with well-calibrated uncertainty quantification, significantly outperforming existing functional regression baselines and achieving competitive or better noisy PDE inverse performance than diffusion-based posterior samplers while reducing test-time sampling cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.22346",
  "author_total": 3,
  "authors": [
    {
      "name": "Yaozhong Shi"
    },
    {
      "name": "Zachary E. Ross"
    },
    {
      "name": "Yisong Yue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnv7ad7kjxgcz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.22346",
  "fulltext_url": null,
  "id": "bnv7ad7kjxgcz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.22346",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7165616499",
  "pdf_url": "https://arxiv.org/pdf/2606.22346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnv7ad7kjxgcz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:58Z",
      "native_id": "2606.22346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.22346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems",
  "title_text": "Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/bnv7ad7kjxgcz",
  "venue": "arXiv",
  "versions": []
}