{
  "abstract": "Diffusion models are increasingly utilized for modeling molecular structures and conformational ensembles, yet the thermodynamic meaning of their learned representations and scores remains elusive. To resolve this ambiguity, we introduce a mathematically consistent action-operator framework natively compatible with diffusion models. By defining a fixed molecular environment as a base action $S_0(x)$ and an alchemical perturbation as an operator $O(x)$, standard diffusion noising induces effective noised actions and operators whose gradients and alchemical derivatives are directly represented by the model's learned fields. This rigorous self-consistency enables a ``noisy operator bridge'' capable of reading out free-energy differences ($ΔF$) from endpoint ensembles and per-frame evaluations. In controlled experiments on alanine dipeptide systems, we show that incorporating physical inductive biases enables partial recovery of the base action and perturbation operator. When applied to a challenging C6-H to C6-F ligand-pocket nonbonded perturbation (185L/IND) with negligible phase-space overlap, our supervised bridge estimates the alchemical $ΔF$ within approximately $1\\ k_\\mathrm{B}T$ of a stable 19-state MBAR reference. Finally, we demonstrate that endpoint coordinates and binary labels alone are sufficient to partially recover the operator shape and a centered free-energy scale without any force or action supervision. This work provides a rigorous path toward transforming generative molecular diffusion models from black-box coordinate samplers into auditable thermodynamic estimators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.30687",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenjie Xi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjsh54dmb3qcv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.30687",
  "fulltext_url": null,
  "id": "fjsh54dmb3qcv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.30687",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "1703|Computational Drug Discovery Methods"
    ]
  ],
  "openalex": "W7166870432",
  "pdf_url": "https://arxiv.org/pdf/2606.30687",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fjsh54dmb3qcv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2606.30687",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.30687"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Unsupervised Thermodynamics of Molecular Diffusion Models: Action-Operator Semantics and Auditable Free-Energy Readout",
  "title_text": "Unsupervised Thermodynamics of Molecular Diffusion Models: Action-Operator Semantics and Auditable Free-Energy Readout",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/fjsh54dmb3qcv",
  "venue": "arXiv",
  "versions": []
}