Beyond Conservation: Flexible Molecular Assembly with Unbalanced Diffusion Bridge

Abstract Molecular assembly (MA) has long been a fundamental task in chemistry and biology, with the potential to create new materials and enable novel functions beyond the molecular scale. However, its vast conformational search space poses substantial challenges, and current generative models remain limited in capturing molecular flexibility and preventing non-physical poses. In this paper, we propose AssemUDB, a diffusion bridge–based framework that learns transport mappings between two distinct flexible domains for molecular assembly generation. We reformulate the marginal matching constraint of diffusion bridges as a coupling distribution governed by unbalanced transport rather than imposing strict conservation. Subsequently, we employ a progressive process from structural relaxation in Euclidean space to assembly on the SE(3) manifold. This relaxation of marginal conservation grants the generative model greater flexibility and leads to more physically plausible atom placements. Comprehensive experiments demonstrate the superior performance of AssemUDB. Notably, we find that the method demonstrates performance comparable to, or even better than, mature tools such as PackMol for packing tasks.