The traditional self organizing map (SOM) is learned by Kohonen learning. The main disadvantage of this approach is in epoch based learning when the radius and rate of learning are decreasing functions of epoch index. The aim of study is to demonstrate advantages of diffusive learning in single epoch learning and other cases for both traditional and anomalous diffusion models. We also discuss the differences between traditional and anomalous learning in models and in quality of obtained SOM. The anomalous diffusion model leads to less accurate SOM which is in accordance to biological assumptions of normal diffusive processes in living nervous system. But the traditional Kohonen learning has been overperformed by novel diffusive learning approaches.