This work introduces GeoDirDock (GDD), a novel approach to molecular docking that enhances the accuracy and physical plausibility of ligand docking predictions. GDD guides the denoising process of a diffusion model along geodesic paths within multiple spaces representing translational, rotational, and torsional degrees of freedom. Our method leverages expert knowledge to direct the generative modeling process, specifically targeting desired protein-ligand interaction regions. We demonstrate that GDD significantly outperforms existing blind docking methods in terms of RMSD accuracy and physicochemical pose realism. Our results indicate that incorporating domain expertise into the diffusion process leads to more biologically relevant docking predictions. Additionally, we explore the potential of GDD for lead optimization in drug discovery through angle transfer in maximal common substructure (MCS) docking, showcasing its capability to predict ligand orientations for chemically similar compounds accurately.
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