The present invention extends to methods, systems, and computer program products for path planning for autonomous moving devices. Aspects of the invention include planning a path for a mobile robot to move autonomously in an environment that includes other static and moving obstacles, such as, for example, other mobile devices and pedestrians, without reference to a prior map of the environment. A planned path for a mobile robot can be determined, adjusted, and adapted using diffusion maps to avoid collisions while making progress towards a global destination. Path planning can include using transition probabilities between grid points to find a feasible path through parts of the environment to make progress towards the global destination. In one aspect, diffusion maps are used in combination with a receding horizon approach, including computing diffusion maps at specified time intervals.