Trajectory data is valuable for applications such as urban planning, but its public availability is often limited by privacy concerns and data collection costs. While recent diffusion models have shown promise in generative tasks, existing methods rarely integrate personalized conditioning with road network constraints. As a result, they struggle to simultaneously achieve personalized mobility modeling and high road-network spatial validity, resulting in limited trajectory quality. In this paper, we propose Sem-RoadDiff, a symmetry-aware dual-guided diffusion model for personalized and road network-constrained trajectory generation. Specifically, our model incorporates two key components. First, we design a semantic preference guidance mechanism to encode user history into a preference-weighted user embedding using a temperature-scaled softmax. This enables the model to capture user-level mobility patterns without directly using raw trip-level records as generation conditions. Second, we introduce a road-aware mechanism to improve overall spatial validity, employing a spatial validity loss derived from the User Mobility Transition Graph. From a symmetry perspective, Sem-RoadDiff aims to preserve distributional symmetry between real and generated trajectories while respecting the inherent asymmetry of directed road-network transitions. Extensive experiments on the Geolife and Porto datasets demonstrate that our approach improves trajectory distributional fidelity compared with the evaluated baselines and improves road-segment connectivity over the diffusion-based baseline.
Zhu et al. (Mon,) studied this question.