Generative modeling provides a powerful framework for learning the complex distributions of three-dimensional molecular structures directly from data [1]. While recent advances in diffusion and flow-based models have demonstrated impressive capabilities for molecular generation, extending these approaches to systems with both molecular flexibility and heterogeneous structural components remains challenging. In particular, protein–ligand complexes exhibit coupled changes in atomic coordinates, molecular geometry, and intermolecular interactions, requiring generative models to capture dependencies across different parts of the molecular system. This project aims to develop a generative framework for three-dimensional protein–ligand modeling based on continuous flow matching and geometric graph learning. We will represent protein–ligand complexes as interacting molecular graphs and employ scalable E(3)-equivariant graph neural networks to learn the evolution of their three-dimensional structures. Rather than treating protein conformational changes and ligand generation as independent problems, the model will learn a joint continuous transformation between different molecular states, including the transition from an apo protein and ligand configuration towards a bound complex. This formulation allows molecular coordinates, local geometric environments, and long-range protein–ligand interactions to be modeled within a unified generative process. A central research question is how the choice of geometric representation affects generative modeling of molecular structures. We will investigate continuous flows in both Euclidean and manifold-based spaces and study whether explicit geometric constraints provide measurable advantages over simpler formulations. Different parameterizations of molecular degrees of freedom, graph message-passing mechanisms, equivariant architectures, and conditioning strategies will be systematically explored. We will further investigate stochastic perturbations and relaxation flows as mechanisms for improving the diversity and structural quality of generated samples. Experiments will initially be conducted on relatively small molecular datasets to enable rapid development and controlled ablation studies, followed by experiments on larger protein–ligand datasets. Evaluation will focus on both the quality of the learned generative distribution and the ability of the model to produce physically and structurally plausible molecular configurations. We will assess structural accuracy, diversity, sampling efficiency, robustness to large conformational changes, and the consistency of the learned continuous trajectories. Multiple generated structures will also be used to investigate learned confidence and ranking mechanisms for selecting high-quality molecular configurations. More broadly, the project seeks to investigate how continuous generative modeling and geometric graph learning can be combined to learn complex distributions of three-dimensional molecular structures. The resulting framework is intended not only as a flexible docking model, but as a general generative modeling approach for structured molecular systems, providing a foundation for future applications in molecular design, structure optimization, and property-guided generation. [1] Zhou. et al. Energy-Based Flow Matching for Generating 3D Molecular Structure