Equivariant Efficient Joint Discrete and Continuous MeanFlow for Molecular Graph Generation

2026-04-09

AI Summary

This work addresses the challenge of jointly modeling discrete topology and continuous geometry in molecular graph generation, a task hindered by heterogeneous distributions, incompatible noise dynamics, and the absence of equivariant inductive biases. Existing approaches often decouple these aspects, leading to physically inconsistent outputs and inefficient sampling. To overcome these limitations, we propose EQUIMF—the first unified SE(3)-equivariant generative framework that integrates synchronous discrete-continuous MeanFlow dynamics. By introducing a unified time bridge and mutually conditioned mean velocity fields, EQUIMF enables highly efficient few-step generation. Our method is the first equivariant generative model to coherently model both graph structure and 3D geometry, achieving substantial improvements over current diffusion and flow-matching approaches in terms of generation quality, physical validity, and sampling efficiency.

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.

Problem

• molecular graph generation
• discrete-continuous joint modeling
• equivariant generative modeling
• flow matching
• geometric deep learning

Innovation

• Equivariant Generative Modeling
• Joint Discrete-Continuous Generation
• MeanFlow
• Molecular Graph Generation
• SE(3) Equivariance