统一建模分子图的拓扑与几何，实现高效物理一致生成
Equivariant Efficient Joint Discrete and Continuous MeanFlow for Molecular Graph Generation
- 通过同步均值流动态联合建模图结构与三维坐标
- 仅需少数步骤即可生成符合物理规律的分子构型
- 适合需要快速生成高质量分子结构的研究者
图结构数据同时包含离散拓扑与连续几何，其异质分布、噪声动态不兼容及等变归纳偏置需求，给生成建模带来根本挑战。现有图生成流匹配方法通常将结构与几何解耦，缺乏跨域同步动态，依赖迭代采样，常导致分子构象物理不一致且生成缓慢。为此，我们提出等变均值流（EQUIMF），一种统一的SE(3)等变生成框架，通过同步均值流动态联合建模离散与连续成分。EQUIMF引入统一时间桥和平均速度更新，并在结构与几何间实现相互条件，支持高效少步生成并保持物理一致性。此外，我们设计了一种新颖的离散均值流形式，采用简单有效的参数化，支持离散图结构上的高效生成。大量实验表明，EQUIMF在生成质量、物理有效性与采样效率上持续优于以往扩散与流匹配方法。
原文摘要 · Abstract (English)
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.
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