Inertial Fragment Matching: scalable shape-conditioned molecular generation via descriptor decomposition

Prior work has demonstrated that three-dimensional molecular structures can be generated effectively using an equivariant diffusion model conditioned on the ordered principal moments of inertia as a compact and interpretable shape descriptor. While guidance of the generation process by this coarse-grained representation enables high shape similarity for relatively small molecules, its limitations become increasingly apparent for larger molecular structures. We introduce Inertial Fragment Matching (IFM), an inference framework that exploits the additivity and reference-point translatability of the moment-of-inertia (MOI) tensor while using its ordered principal moments as the model-facing conditioning signal. IFM enables fragment-based molecular generation while preserving global shape consistency, substantially improving generation quality and scalability for generation of larger molecules. IFM achieves an average shape similarity of 0.698, corresponding to a 27.8% improvement over the conventional generation workflow. Under fixed-fragment generation conditions, IFM further attains a fragment integration success rate of 0.638, a 73.8% improvement over conventional inpainting-based approaches. Additionally, the impact of IFM on molecular quality, structural fidelity, and inference efficiency is evaluated. We present a proof of concept for context-window-independent molecular generation by combining inertial fragment matching with chain merging, demonstrating the potential to generate linear molecular chains of arbitrary size. Finally we formulate a general transport-additive fragment matching beyond the molecule generation task.