Automated parking is a critical feature of Advanced Driver Assistance Systems (ADAS), where accurate trajectory prediction is essential to bridge perception and planning modules. Despite its significance, research in this domain remains relatively limited, with most existing studies concentrating on single-modal trajectory prediction of vehicles. In this work, we propose ParkDiffusion, a novel approach that predicts the trajectories of both vehicles and pedestrians in automated parking scenarios. ParkDiffusion employs diffusion models to capture the inherent uncertainty and multi-modality of future trajectories, incorporating several key innovations. First, we propose a dual map encoder that processes soft semantic cues and hard geometric constraints using a two-step cross-attention mechanism. Second, we introduce an adaptive agent type embedding module, which dynamically conditions the prediction process on the distinct characteristics of vehicles and pedestrians. Third, to ensure kinematic feasibility, our model outputs control signals that are subsequently used within a kinematic framework to generate physically feasible trajectories. We evaluate ParkDiffusion on the Dragon Lake Parking (DLP) dataset and the Intersections Drone (inD) dataset. Our work establishes a new baseline for heterogeneous trajectory prediction in parking scenarios, outperforming existing methods by a considerable margin.