Distribution shifts over time are common in real-world machine-learning applications. This scenario is formulated as Evolving Domain Generalization (EDG), where models aim to generalize well to unseen target domains in a time-varying system by learning and leveraging the underlying evolving pattern of the distribution shifts across domains. However, existing methods encounter challenges due to the limited number of timestamps (every domain corresponds to a timestamp) in EDG datasets, leading to difficulties in capturing evolving dynamics and risking overfitting to the sparse timestamps, which hampers their generalization and adaptability to new tasks. To address this limitation, we propose a novel approach SDE-EDG that collects the Infinitely Fined-Grid Evolving Trajectory (IFGET) of the data distribution with continuous-interpolated samples to bridge temporal gaps (intervals between two successive timestamps). Furthermore, by leveraging the inherent capacity of Stochastic Differential Equations (SDEs) to capture continuous trajectories, we propose their use to align SDE-modeled trajectories with IFGET across domains, thus enabling the capture of evolving distribution trends. We evaluate our approach on several benchmark datasets and demonstrate that it can achieve superior performance compared to existing state-of-the-art methods.