In recent years, the volume of captured location-based movement data has drastically increased with the prevalence of smartphones. Mobility data are commonly used for smart assistant and personalized advertising applications. However, such data contain considerable sensitive information; thus, they must be anonymized before they can be published or analyzed. In this study, we investigate the problem of anonymization for trajectory publication. Anonymizing trajectories is challenging because they have high dimensionality in both the spatial and temporal domains. Traditional anonymization methods cannot handle high dimensionality without significantly sacrificing data utility. The proposed method addresses this limitation by training a Seq2Seq autoencoder model to reconstruct trajectories from the spatiotemporal input, followed by distributing the Laplace noise to the principal components of the Seq2Seq encoder's hidden-layer output under differential privacy. By distributing the privacy budget in the latent space, the proposed method can output trajectories that satisfy differential privacy while maintaining embedded information. Experimental results from the application of the proposed method to real-life movement trajectory data from Saitama, Japan, demonstrate a reduction in data loss by up to 75.7 % while maintaining significant data utility.