Multi-agent trajectory prediction is crucial for various practical applications, spurring the construction of many large-scale trajectory datasets, including vehicles and pedestrians. However, discrepancies exist among datasets due to external factors and data acquisition strategies. External factors include geographical differences and driving styles, while data acquisition strategies include data acquisition rate, history/prediction length, and detector/tracker error. Consequently, the proficient performance of models trained on large-scale datasets has limited transferability on other small-size datasets, bounding the utilization of existing large-scale datasets. To address this limitation, we propose a method based on continuous and stochastic representations of Neural Stochastic Differential Equations (NSDE) for alleviating discrepancies due to data acquisition strategy. We utilize the benefits of continuous representation for handling arbitrary time steps and the use of stochastic representation for handling detector/tracker errors. Additionally, we propose a dataset-specific diffusion network and its training framework to handle dataset-specific detection/tracking errors. The effectiveness of our method is validated against state-of-the-art trajectory prediction models on the popular benchmark datasets: nuScenes, Argoverse, Lyft, INTERACTION, and Waymo Open Motion Dataset (WOMD). Improvement in performance gain on various source and target dataset configurations shows the generalized competence of our approach in addressing cross-dataset discrepancies.