Few results for state estimation, or observer design, for nonlinear distributed parameter systems exist. The most practical approach is to approximate the solution to the corresponding partial differential equation and use a method for estimation of nonlinear ordinary differential equations. A comparison of different popular observation techniques - Unscented Kalman filter (UKF), extended kalman filtering (EKF), and new nonlinear version of sliding mode observer (SMO) - is conducted. The proposed nonlinear SMO combines the efficiency of a nonlinear observer with the robustness of the SMO. The estimation of linear, a quasi-linear and nonlinear diffusion equations is considered. The simulation results show good performance of the UKF and EKF in the absence of disturbances. However, the nonlinear SMO performs better when disturbances exist.