{
  "abstract": "Brownian stochastic interpolants connect paired endpoint samples, yet their sampling error can depend on displacement moments even when neither endpoint has a first moment. For arbitrary Borel couplings, we prove early-stopped, target-to-output KL guarantees for standard Euler sampling from the true source. A fourth displacement moment gives an explicit $O(N^{-1})$ bound; a second moment suffices for fixed-law convergence as drift error vanishes. For one fixed coupling with no displacement moment above two, original bridge-path KL stays of order one, comparison-path KL is of order $1/\\log N$, and terminal KL is at most $C/N^2$ on the same grid. The path decomposition identifies the information about the source discarded by Markov projection. When the original bridge is Markov, current-state Euler sampling instead has a second-moment $O((M_2+d)/N)$ bound; finite-entropy Schroedinger bridges for the probability Brownian reference are included. We also construct a current-state learner with expected output KL consistency from iid endpoint pairs. Numerical diagnostics illustrate the distinct errors. Conditional diffusion identities specify a restoration interface, while image controls find no iterative advantage over cheap probabilistic predictors. Uniform terminal rates for general second-moment couplings remain open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37413",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhong Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43nd7rmd3dnyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37413",
  "fulltext_url": null,
  "id": "43nd7rmd3dnyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37413",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7224115339",
  "pdf_url": "https://arxiv.org/pdf/2610.37413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43nd7rmd3dnyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Displacement Moments and Path-Terminal Separation in Brownian Interpolant Sampling",
  "title_text": "Displacement Moments and Path-Terminal Separation in Brownian Interpolant Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/43nd7rmd3dnyk",
  "venue": "arXiv",
  "versions": []
}