Recent progress in interactive point prompt based Image Segmentation allows to significantly reduce the manual effort to obtain high quality semantic labels.State-of-the-art unsupervised methods use self-supervised pre-trained models to obtain pseudo-labels which are used in training a prompt-based segmentation model.In this paper, we propose a novel unsupervised and training-free approach based solely on the self-attention of Stable Diffusion.We interpret the self-attention tensor as a Markov transition operator, which enables us to iteratively construct a Markov chain.Pixel-wise counting of the required number of iterations along the Markov chain to reach a relative probability threshold yields a Markov-iteration-map, which we simply call a Markov-map.Compared to the raw attention maps, we show that our proposed Markov-map has less noise, sharper semantic boundaries and more uniform values within semantically similar regions.We integrate the Markov-map in a simple yet effective truncated nearest neighbor framework to obtain interactive point prompt based segmentation.Despite being training-free, we experimentally show that our approach yields excellent results in terms of Number of Clicks (NoC), even outperforming state-of-the-art training based unsupervised methods in most of the datasets.