Transport-Coupled Bayesian Flows for Molecular Graph Generation (TopBF) addresses a key mismatch in existing diffusion models for molecular graph generation by eliminating the need for hard discretization during sampling. The framework generates graphs directly in continuous parameter distributions, learns graph topology via a Quasi-Wasserstein optimal‑transport coupling with geodesic costs, and enables property‑conditioned generation without retraining. Experiments on QM9 and ZINC250k show that TopBF achieves higher structural fidelity and more efficient generation compared to prior methods.
By Yida Xiong, Jiameng Chen, Kun Li, Hongzhi Zhang, Xiantao Cai, Lei Lei, Wenbin Hu
arXiv:2603. 10395v2 Announce Type: replace Abstract: Graph generation is a fundamental task with broad applications, such as drug discovery.
By Baoheng Zhu, Deyu Bo, Delvin Ce Zhang, Xiao Wang
arXiv:2605. 15354v2 Announce Type: replace Abstract: Despite the success of foundation models in language and vision, molecular graph generation still lacks a unified framework for heterogeneous design tasks with reliable controllability.
By Yihan Zhu, Yuhan Liu, Weijiang Li, Tengfei Luo, Meng Jiang
The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.
By Yixuan Sun, Anirban Samaddar, Sandeep Madireddy
The paper introduces Gromov-Monge Flow Matching, a method that incorporates permutation-equivariance into generative graph models by aligning graph pairs up to node relabeling using the Gromov–Monge distance. It shows theoretically that quotient couplings can be lifted to aligned representatives without extra cost and that symmetrization yields equivariant flow-matching minimizers, even for categorical endpoints. Practically, the authors build minibatch couplings with Gromov–Wasserstein relaxations and optional outer assignments, improving sample quality in continuous graph and categorical molecular generation while remaining compatible with standard equivariant architectures.
By Moritz Piening, Christian Wald
The paper introduces Variational Bayesian Flow Network (VBFN), a graph generation model that lifts Bayesian updates to a joint Gaussian belief family with structured precisions, enabling coupled node and edge updates in a single fusion step. By constructing sample‑agnostic sparse precisions from a representation‑induced dependency graph, VBFN avoids label leakage while enforcing node‑edge consistency. Experiments on synthetic and molecular graph datasets show that VBFN improves fidelity and diversity over baseline methods.
By Yida Xiong, Jiameng Chen, Xiuwen Gong, Jia Wu, Shirui Pan, Wenbin Hu
arXiv:2605. 31498v2 Announce Type: replace Abstract: A long standing challenge in computational chemistry and biophysics is efficiently sampling the Boltzmann distribution of molecules.
By Daniel Pe\~naherrera, Rishal Aggarwal, David Ryan Koes
Exploring the chemical space of flexible molecules remains challenging because the vast number of possible compounds and conformations, together with the increasing cost and limited generalization of...
arXiv:2607. 19519v1 Announce Type: cross Abstract: Most 3D properties relevant to molecular design, including free energies and shape descriptors, are $\textit{expectations}$ over the Boltzmann distribution over 3D configurations of a molecular graph.
By Selma Moqvist, Richard Beckmann, Ross Irwin, Roc\'io Mercado, Simon Olsson
arXiv:2602. 18695v2 Announce Type: replace Abstract: Existing insertion-based masked diffusion models that generate sequences by interleaving token insertion with unmasking use fixed schedules that are not dependent on the data.
By Dhruvesh Patel, Benjamin Rozonoyer, Gaurav Pandey, Tahira Naseem, Ram\'on Fernandez Astudillo, Andrew McCallum
LapDDPM is a conditional Graph Diffusion Probabilistic Model that generates high‑fidelity, biologically plausible single‑cell RNA sequencing data. It incorporates graph‑based inductive biases and a spectral adversarial perturbation mechanism to enforce robustness against structural noise, effectively acting as a Distributionally Robust Optimization framework. The model extends to spatial transcriptomics and multi‑modal data, and experimental results on datasets such as PBMC3K, Dentate Gyrus, HLCA, Visium, and 10x Multiome show it outperforms state‑of‑the‑art baselines in distribution matching, manifold preservation, and downstream utility.
By Lorenzo Bini, Stephane Marchand-Maillet
arXiv:2605. 00337v2 Announce Type: replace Abstract: Sampling the distribution of collective variables (CVs) and estimating the associated free energy surface are crucial problems in statistical physics, as they underpin a better understanding of chemical reactions and conformational transitions.
By Zichen Liu, Tiejun Li