In this paper, a novel solution for autonomous robotic exploration is proposed. The distribution of information in an unknown environment is modeled as an unsteady diffusion process, which can be an appropriate mathematical formulation and analogy for expanding, time-varying, and dynamic environments. This information distribution map is the solution of the diffusion process partial differential equation, and is regressed from sensor data as a Gaussian Process. Optimization of the process parameters leads to an optimal frontier map which describes regions of interest for further exploration. Since the presented approach considers a continuous model of the environment, it can be used to plan smooth exploration paths exploiting the structural dependencies of the environment whilst handling sparse sensors measurements. The performance of the proposed approach is evaluated through simulation results in the well-known Freiburg and Cave maps
