  Trajectory data is essential for various applications as it records the
movement of vehicles. However, publicly available trajectory datasets remain
limited in scale due to privacy concerns, which hinders the development of
trajectory data mining and trajectory-based applications. To address this
issue, some methods for generating synthetic trajectories have been proposed to
expand the scale of the dataset. However, all existing methods generate
trajectories in the geographical coordinate system, which poses two limitations
for their utilization in practical applications: 1) the inability to ensure
that the generated trajectories are constrained on the road. 2) the lack of
road-related information. In this paper, we propose a new problem to meet the
practical application need, \emph{i.e.}, road network-constrained trajectory
(RNTraj) generation, which can directly generate trajectories on the road
network with road-related information. RNTraj is a hybrid type of data, in
which each point is represented by a discrete road segment and a continuous
moving rate. To generate RNTraj, we design a diffusion model called
Diff-RNTraj. This model can effectively handle the hybrid RNTraj using a
continuous diffusion framework by incorporating a pre-training strategy to
embed hybrid RNTraj into continuous representations. During the sampling stage,
a RNTraj decoder is designed to map the continuous representation generated by
the diffusion model back to the hybrid RNTraj format. Furthermore, Diff-RNTraj
introduces a novel loss function to enhance the spatial validity of the
generated trajectories. Extensive experiments conducted on two real-world
trajectory datasets demonstrate the effectiveness of the proposed model.
