{
  "abstract": "Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling. However, performing posterior inference with such priors is challenging because their induced function-space distributions are typically not available in closed form. One practical strategy is to approximate the prior using a finite collection of sampled functions, and then represent posterior functions as learned combinations of these samples. Existing approaches commonly place a Gaussian variational distribution over the combination weights. While tractable, this choice limits the shapes of posterior uncertainty that can be represented, especially when the true posterior is asymmetric, heavy-tailed, or multimodal. We propose Flow-Transformed Implicit Processes (FTIP), a variational inference method that makes this finite-dimensional function-space approximation more expressive. Instead of using a Gaussian distribution over the combination weights, FTIP uses a normalizing flow to define a richer variational distribution. This induces a flexible posterior distribution over functions while preserving tractable optimization. We train the model using a Black-Box α objective, allowing us to compare mass-covering and mode-seeking variational behaviour. Experiments show that FTIP captures asymmetric and multimodal posterior structure in function space that Gaussian coefficient approximations tend to smooth or collapse.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.01954",
  "author_total": 3,
  "authors": [
    {
      "name": "Luis A. Ortega"
    },
    {
      "name": "Andrés R. Masegosa"
    },
    {
      "name": "Thomas D. Nielsen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mx6mzgmrk5jg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.01954",
  "fulltext_url": null,
  "id": "8mx6mzgmrk5jg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.01954",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7163126355",
  "pdf_url": "https://arxiv.org/pdf/2606.01954",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mx6mzgmrk5jg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:32Z",
      "native_id": "2606.01954",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.01954"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Flow-Transformed Implicit Processes for Function-Space Variational Inference",
  "title_text": "Flow-Transformed Implicit Processes for Function-Space Variational Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/8mx6mzgmrk5jg",
  "venue": "arXiv",
  "versions": []
}