MOTIVATION: Structure-based drug design (SBDD) has advanced with deep generative models, but bridging the gap between continuous atomic coordinates and discrete atom types remains a challenge. Current approaches, such as diffusion and flow matching models, often fail to unify these heterogeneous modalities, relying on separate strategies or ill-fitting Euclidean metrics for discrete variables. This lack of a consistent framework limits generative models' ability to capture the geometric and chemical structure of protein-ligand complexes. RESULTS: We present MolPIF, a parameter interpolation flow mechanism designed to unify the generation of continuous and discrete molecular variables. Unlike traditional flow models that operate in sample space, MolPIF interpolates between distributions in the parameter space, theoretically recovering Wasserstein-2 optimal transport for continuous coordinates and establishing Fisher-Rao geodesics for discrete atom types. We further incorporate a geometry-enhanced learning strategy to improve the capture of atomic contexts. Extensive evaluations on the CrossDocked2020 dataset demonstrate that MolPIF outperforms baselines in binding affinity, chemical validity, geometric fidelity, and chemical space coverage. Additionally, MolPIF exhibits versatility in lead optimization and offers flexible prior distribution selection (such as Laplace), establishing a robust paradigm for SBDD. AVAILABILITY AND IMPLEMENTATION: Source code is freely available at https://github.com/BLEACH366/MolPIF.

Structure-Based Drug Design (SBDD) is crucial for identifying bioactive molecules. Recent deep generative models are faced with challenges in geometric structure modeling. A major bottleneck lies in the twisted probability path of multi-modalities—continuous 3D positions and discrete 2D topologies—which jointly determine molecular geometries. By establishing the fact that noise schedules decide the Variational Lower Bound (VLB) for the twisted probability path, we propose VLB-Optimal Scheduling (VOS) strategy in this under-explored area, which optimizes VLB as a path integral for SBDD. Our model effectively enhances molecular geometries and interaction modeling, achieving state-of-the-art PoseBusters passing rate of 95.9\% on CrossDock, more than 10\% improvement upon strong baselines, while maintaining high affinities and robust intramolecular validity evaluated on held-out test set. Code is available at https://github.com/AlgoMole/MolCRAFT.