The evaluation of AI-based medium-range weather forecast models commonly relies on pointwise error metrics such as the root-mean-square error (RMSE), which provide useful quantitative summaries but do not directly show how multivariate forecast states evolve in relation to the observed atmospheric state. This study proposes a trajectory-based diagnostic framework built on a topology-preserving state space for visually and quantitatively comparing forecast behavior across different AI weather forecast models. Multivariate atmospheric states are represented using 850 hPa temperature, geopotential height, zonal wind, and meridional wind fields, and a shared state space is constructed through image-based feature extraction, contrastive learning, and manifold embedding. The framework is applied to forecasts from FourCastNet2, GraphCast, and Pangu-Weather under different initial-condition settings, with forecast sequences represented as trajectories in the learned state space. The results show that the proposed representation provides an intuitive way to compare model-dependent forecast evolution, identify regions of relatively good or poor trajectory behavior, and examine state- or season-dependent differences that are not readily summarized by variable-wise RMSE curves alone. The proposed framework is therefore intended as a complementary diagnostic tool for interpreting AI-based weather forecast models, rather than as a replacement for conventional verification metrics.