Functional rehabilitation training relies on accurate execution of point-to-point movements such as stretching, flexing, and lifting, which are crucial for achieving functional recovery. To ensure patients perform these movements precisely, it is important to model them accurately. Although stable dynamical systems are traditionally employed due to their convergence properties, they often model these movements deterministically, neglecting the variability and uncertainties inherent in rehabilitation scenarios, such as external noise and imperfections in therapist demonstrations. To address these challenges, this paper proposes a novel method for constructing a family of stochastic dynamical systems that maintain desired convergence properties while enhancing robustness and adaptability. We introduce a mechanism incorporating a learnable rank-one correlation with a latent variable, allowing for accurate modeling of the dynamical system’s distribution. Through minimizing demonstration learning loss and Kullback-Leibler divergence, our model achieves effective end-to-end training. We demonstrate the efficacy of our approach through simulations and real-world applications in robot-assisted point-to-point functional rehabilitation tasks, showcasing its potential to improve rehabilitation training by accommodating the dynamic variability of patient performance and therapeutic settings.