Equivariant Efficient Joint Discrete and Continuous MeanFlow for Molecular Graph Generation

TL;DR

EQUIMF is a novel SE(3)-equivariant generative framework that jointly models discrete molecular structure and continuous geometry, enabling efficient, physically consistent molecule generation.

Contribution

It introduces a unified, synchronized MeanFlow approach for joint discrete and continuous molecular graph generation, improving efficiency and physical validity.

Findings

Outperforms prior methods in generation quality and physical validity.

Enables efficient few-step molecule generation.

Supports effective discrete structure modeling with a new MeanFlow formulation.

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.