{"ID":5439706,"CreatedAt":"2026-07-01T01:17:58.482524686Z","UpdatedAt":"2026-07-01T14:22:42.384190123Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.30687","arxiv_id":"2606.30687","title":"Unsupervised Thermodynamics of Molecular Diffusion Models: Action-Operator Semantics and Auditable Free-Energy Readout","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.","short_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 dif...","url_abs":"https://arxiv.org/abs/2606.30687","url_pdf":"https://arxiv.org/pdf/2606.30687v1","authors":"[\"Wenjie Xi\"]","published":"2026-06-28T14:45:31Z","proceeding":"physics.chem-ph","tasks":"[\"physics.chem-ph\",\"cond-mat.stat-mech\",\"cs.AI\"]","methods":"[\"Diffusion Model\",\"Generative Adversarial Network\"]","has_code":false}