Equivariant Efficient Joint Discrete and Continuous MeanFlow for Molecular Graph Generation
2026-04-09 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the challenge of generating graph data that includes both discrete parts (like connections between nodes) and continuous parts (like the positions of atoms). Previous methods treated these parts separately, causing slow sampling and less accurate results. They propose EQUIMF, a new approach that models both parts together in a synchronized way, which leads to faster and more physically accurate generation. Their experiments show that EQUIMF works better than existing methods in quality, speed, and producing physically valid structures.
graph generationdiscrete topologycontinuous geometryflow-matchingSE(3)-equivarianceMeanFlow dynamicsmolecular conformationsampling efficiencydiffusion modelsinductive biases
Authors
Rongjian Xu, Teng Pang, Zhiqiang Dong, Guoqiang Wu
Abstract
Graph-structured data jointly contain discrete topology and continuous geometry, which poses fundamental challenges for generative modeling due to heterogeneous distributions, incompatible noise dynamics, and the need for equivariant inductive biases. Existing flow-matching approaches for graph generation typically decouple structure from geometry, lack synchronized cross-domain dynamics, and rely on iterative sampling, often resulting in physically inconsistent molecular conformations and slow sampling. To address these limitations, we propose Equivariant MeanFlow (EQUIMF), a unified SE(3)-equivariant generative framework that jointly models discrete and continuous components through synchronized MeanFlow dynamics. EQUIMF introduces a unified time bridge and average-velocity updates with mutual conditioning between structure and geometry, enabling efficient few-step generation while preserving physical consistency. Moreover, we develop a novel discrete MeanFlow formulation with a simple yet effective parameterization to support efficient generation over discrete graph structures. Extensive experiments demonstrate that EQUIMF consistently outperforms prior diffusion and flow-matching methods in generation quality, physical validity, and sampling efficiency.