{
  "abstract": "Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference---Markov chain Monte Carlo (MCMC)---is sequential, yields correlated samples, and must be rerun for each new observation. Conditional flow matching offers an amortized alternative: a transport map, trained once on joint samples of parameter and data, that yields independent approximate posterior samples for any observation at negligible online cost, without new likelihood evaluations. We give a careful, MCMC-literate assessment of flow matching for PDE-based inverse problems with function-valued parameters. Exploiting the flow's tractable density, we derive computable accuracy estimates for the learned posterior in total variation distance and Kullback--Leibler divergence and, moreover, propose a hybrid sampler that is made asymptotically exact by Metropolization. We validate the accuracy estimates and demonstrate amortization in several numerical examples, including electrical impedance tomography and a likelihood-free Lotka--Volterra model. Flow matching reproduces posterior means and credible bands closely at a fraction of the forward solves required by MCMC, but its accuracy degrades for concentrated posteriors and for observations that are atypical under the prior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02377",
  "author_total": 4,
  "authors": [
    {
      "name": "Jan Blechschmidt"
    },
    {
      "name": "Oliver G. Ernst"
    },
    {
      "name": "Moritz Poguntke"
    },
    {
      "name": "Björn Sprungk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0x83w9w3k9dyt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02377",
  "fulltext_url": null,
  "id": "0x83w9w3k9dyt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02377",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7220462101",
  "pdf_url": "https://arxiv.org/pdf/2610.02377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0x83w9w3k9dyt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.02377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02377"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems",
  "title_text": "Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/0x83w9w3k9dyt",
  "venue": "arXiv",
  "versions": []
}