{
  "abstract": "In many settings involving stochastic differential equations (SDEs), including diffusion based generative AI, our aim is to accurately generate samples from a distribution. Typically, this is done by generating i.i.d. samples of the SDE. Given a fixed simulation budget, a reasonable way to gain efficiency may be to instead generate a tree of paths through appropriately split partial paths. This suggests improved performance, but one worries about the injected dependence. In this paper, we study this issue comprehensively. We develop a general method to construct the splitting design and analyze its performance for a broad class of error measures, giving insight into the elegant underlying structure in the problem. For the Kolmogorov-Smirnov (KS) distance and maximum mean discrepancy (MMD), we identify the limiting errors of the associated empirical distributions as the simulation budget increases to infinity. We characterize a splitting strategy motivated by a corresponding asymptotic optimization problem. Overall, we observe a 12-26% improvement in mean KS over i.i.d. samples in many settings. On CIFAR-10 and FFHQ, splitting lowers the MMD by 17-26% relative to i.i.d. samples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12513",
  "author_total": 2,
  "authors": [
    {
      "name": "Rushil Gupta"
    },
    {
      "name": "Sandeep Juneja"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/414js3rmffxjp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12513",
  "fulltext_url": null,
  "id": "414js3rmffxjp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12513",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7212612559",
  "pdf_url": "https://arxiv.org/pdf/2609.12513",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/414js3rmffxjp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2609.12513",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12513"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "A Splitting Method for SDE Terminal-Law Estimation",
  "title_text": "A Splitting Method for SDE Terminal-Law Estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/414js3rmffxjp",
  "venue": "arXiv",
  "versions": []
}