{
  "abstract": "We address the problem of learning generative priors over high-dimensional latent variables from indirect, noisy observations, with a focus on continuous heterogeneity in cryo-electron microscopy (cryo-EM). In this setting, 3D atomic structures $x \\in \\mathbb{R}^{3N_a}$ are never directly observed and must be inferred from 2D projection images $y$ generated by a complex, non-linear forward operator. We propose Empirical Bayes Flow Matching (EB-FM), a method that learns a flow matching prior $p_θ(x)$ directly from observations using a Monte Carlo stochastic approximation Expectation-Maximization framework. EB-FM alternates between an E-step that performs approximate posterior sampling from $p_θ(x \\mid y)$ via guided flow-based generation while maintaining persistent latent estimates through stochastic approximation, and an M-step that updates the flow model using these stabilized latent variables as training targets. This approach eliminates the need for pretraining on clean data and naturally accommodates non-linear forward models. We validate our method on controlled inverse problems using two-moons and MNIST data, and demonstrate its effectiveness on simulated cryo-EM data with known poses, showing that EB-FM can recover continuous distributions of protein conformations directly in atomic-coordinate space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05202",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel Aibinder"
    },
    {
      "name": "Azmi Haider"
    },
    {
      "name": "Dan Rosenbaum"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enja2z383ezrt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05202",
  "fulltext_url": null,
  "id": "enja2z383ezrt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05202",
  "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",
      "q-bio.BM"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05202",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enja2z383ezrt.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:30Z",
      "native_id": "2611.05202",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05202"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "arxiv:q-bio.BM",
      "subfield": "biophysics"
    }
  ],
  "title": "Empirical Bayes Flow Matching for Continuous Cryo-EM Heterogeneity",
  "title_text": "Empirical Bayes Flow Matching for Continuous Cryo-EM Heterogeneity",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:04Z",
  "url": "https://research.draconitic.com/paper/enja2z383ezrt",
  "venue": "arXiv",
  "versions": []
}