This paper presents Latent Adaptive Planner (LAP), a novel approach for dynamic nonprehensile manipulation tasks that formulates planning as latent space inference, effectively learned from human demonstration videos. Our method addresses key challenges in visuomotor policy learning through a principled variational replanning framework that maintains temporal consistency while efficiently adapting to environmental changes. LAP employs Bayesian updating in latent space to incrementally refine plans as new observations become available, striking an optimal balance between computational efficiency and real-time adaptability. We bridge the embodiment gap between humans and robots through model-based proportional mapping that regenerates accurate kinematic-dynamic joint states and object positions from human demonstrations. Experimental evaluations across multiple complex manipulation benchmarks demonstrate that LAP achieves state-of-the-art performance, outperforming existing approaches in success rate, trajectory smoothness, and energy efficiency, particularly in dynamic adaptation scenarios. Our approach enables robots to perform complex interactions with human-like adaptability while providing an expandable framework applicable to diverse robotic platforms using the same human demonstration videos.