{
  "abstract": "Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models, recasting predictive sampling as an ODE with closed-form Gaussian dynamics and a likelihood-dependent guidance term that admits a simple Monte Carlo approximation. In the linear-Gaussian setting, we recover standard GP conditioning exactly; beyond conjugacy, the same machinery handles any conditioning statement admitting point-wise likelihood evaluation - including non-linear physics, and, for the first time, natural language via large language models. Whitening isolates the irreducible non-Gaussian dynamics, minimising Wasserstein-2 transport cost and eliminating numerical stiffness. The result is a general-purpose GP inference scheme requiring no bespoke derivations. Together, these results provide a general mechanism for incorporating the full richness of real-world knowledge as conditioning information, opening a new frontier for the probabilistic modelling of real-world problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.21041",
  "author_total": 8,
  "authors": [
    {
      "name": "Henry Moss"
    },
    {
      "name": "Lachlan Astfalck"
    },
    {
      "name": "Thomas Cowperthwaite"
    },
    {
      "name": "Colin Doumont"
    },
    {
      "name": "Sam Willis"
    },
    {
      "name": "Philipp Hennig"
    },
    {
      "name": "Christopher Nemeth"
    },
    {
      "name": "Andrew Zammit-Mangion"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/026wpae5aw9jx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21041",
  "fulltext_url": null,
  "id": "026wpae5aw9jx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.21041",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7162021825",
  "pdf_url": "https://arxiv.org/pdf/2605.21041",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/026wpae5aw9jx.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:21Z",
      "native_id": "2605.21041",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21041"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Conditioning Gaussian Processes on Almost Anything",
  "title_text": "Conditioning Gaussian Processes on Almost Anything",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/026wpae5aw9jx",
  "venue": "arXiv",
  "versions": []
}