{
  "abstract": "Bayesian flow networks (BFNs) jointly model atomic coordinates and atom types for structure-based drug design, but their generative dynamics remain poorly understood. We show that the two channels resolve on different terms: atom types pass through a sharp commitment transition at tc1, whereas coordinate precision improves smoothly with no critical point of its own, reaching sub-Ångstrom resolution only at a stated threshold tc2. Extreme-value theory predicts the type channel's posterior half-maximum in closed form, and the predicted 1/β1 scaling holds across seven β1 values (R2 = 0.996) and over 13 points spanning three BFN architectures and two domains, though measured times run 11%-20% below the predicted absolute values. Exploiting that structure, phase-aware iterative refinement aligns three rounds to these boundaries and trains no auxiliary regressor, reward function, or property predictor. On 100 CrossDocked2020 test pockets at K = 200, it reaches a mean Vina Dock of -8.72 kcal/mol. Gradient-guided methods that need such training stay ahead by a small margin: over the 100-pocket intersection, the paired gap to MolJO (-8.98) is 0.25 kcal/mol (95% CI [-0.13, +0.60], paired Wilcoxon p = 0.022); equivalence testing at a preregistered ±0.5 kcal/mol margin does not establish equivalence within it. CByG (-9.16) leads by 0.44 kcal/mol on unpaired means. Phase-aware iteration improves the Round-1 to Round-3 mean by 1.34 kcal/mol (paired Wilcoxon p = 4.80 × 10-18, Cohen's dz = -1.59) and shifts the median by -1.44 kcal/mol, a shift Best-of-K resampling cannot produce. Paired on the pocket, an audited rerun passes every PoseBusters check 4.7 percentage points more often than MolJO.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Obstetrics and Biomedical Innovation Center, the Sixth Affiliated Hospital of Sun Yat-sen University, No. 26 of Yuancun Second Cross Road, Guangzhou510655Guangdong, China."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 9,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Liangji Zhou",
      "orcid": "0009-0007-6742-6320"
    },
    {
      "affs": [
        0
      ],
      "name": "Yuanqiu Chen"
    },
    {
      "affs": [
        0
      ],
      "name": "Tongtong Chen"
    },
    {
      "affs": [
        0
      ],
      "name": "Yijuan Huang"
    },
    {
      "affs": [
        0
      ],
      "name": "Qihao Pan"
    },
    {
      "affs": [
        0
      ],
      "name": "Si Li"
    },
    {
      "affs": [
        0
      ],
      "name": "Chenyu Gou"
    },
    {
      "affs": [
        0
      ],
      "name": "Meiqiong Fan"
    },
    {
      "affs": [
        0
      ],
      "name": "Yu Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdze1jgdma96e.bib",
  "cited_by": 0,
  "doi": "10.1021/acs.jcim.6c01538",
  "fulltext_url": "https://europepmc.org/articles/PMC13663863",
  "id": "fdze1jgdma96e",
  "issns": [
    "1549-9596",
    "1549-960X"
  ],
  "landing_url": "https://europepmc.org/article/MED/42912920",
  "language": "eng",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1703|Computational Drug Discovery Methods"
    ]
  ],
  "openalex": "W7214009500",
  "pdf_url": "https://europepmc.org/articles/PMC13663863?pdf=render",
  "pmcid": "PMC13663863",
  "pmid": "42912920",
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdze1jgdma96e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:14Z",
      "native_id": "MED:42912920",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42912920"
    }
  ],
  "subjects": [],
  "title": "Hierarchical Phase Transitions in Bayesian Flow Networks Enable Training-Free Molecular Design.",
  "title_text": "Hierarchical Phase Transitions in Bayesian Flow Networks Enable Training-Free Molecular Design.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:20:14Z",
  "url": "https://research.draconitic.com/paper/fdze1jgdma96e",
  "venue": "Journal of chemical information and modeling",
  "versions": []
}