Positron emission tomography (PET) images are corrupted by noise. This is especially true in dynamic PET imaging where short frames are required to capture the peak of activity concentration after the radiotracer injection. High noise results in a possible bias in quantification, as the compartmental models used to estimate the kinetic parameters are sensitive to noise. This paper describes a new post-reconstruction filter to increase the signal-to-noise ratio in dynamic PET imaging. It consists in a spatio-temporal robust diffusion of the 4D image based on the time activity curve (TAC) in each voxel. It reduces the noise in homogeneous areas while preserving the distinct kinetics in regions of interest corresponding to different underlying physiological processes. Neither anatomical priors nor the kinetic model are required. We propose an automatic selection of the scale parameter involved in the diffusion process based on a robust statistical analysis of the distances between TACs. The method is evaluated using Monte Carlo simulations of brain activity distributions. We demonstrate the usefulness of the method and its superior performance over two other post-reconstruction spatial and temporal filters. Our simulations suggest that the proposed method can be used to significantly increase the signal-to-noise ratio in dynamic PET imaging.