Demystifying Multimodal Biomolecular Co-design With Intrinsic Geodesic Coupling

Biomolecules such as proteins and small-molecule ligands play a central role in biological systems, arising from the tight interplay between sequence and three-dimensional structure. Recent generative models for biomolecular co-design aim to capture this interplay by jointly modeling coupled modalities. However, existing approaches largely adopt a parallel execution of marginal generative processes, implicitly enforcing fixed synchronous coupling. We argue that a critical but overlooked degree of freedom lies in how these marginal processes are \emph{temporally coupled} during training and generation, where inappropriate coupling can introduce high-variance supervision and inconsistent intermediate states, affecting modality consistency. To address this, we introduce GeoCoupling, a systematic framework that optimizes for temporal couplings between heterogeneous modalities. Empirical results across structure-based drug design and unconditional protein design demonstrate the learned couplings consistently outperform synchronous and randomly coupled baselines, yielding biomolecules with improved physical validity and diversity.

Many biological design problems involve combining different kinds of information, such as a molecule’s sequence and its 3D structure. We show that a hidden challenge in current multimodal generative models is that these different parts often do not evolve well together during generation. To address this, we develop GeoCoupling, a general method that learns how to better coordinate multiple data types over time instead of relying on hand-designed schedules. Across protein design and drug design tasks, this leads to generated molecules that are more physically realistic, more internally consistent, and more diverse than those produced by existing approaches.