Diffusion of molecules in living cell membranes is influenced by several factors, such as interactions with other molecules and the characteristics of their environment. By observing the diffusion of biomolecules, we can study their interaction and hence function during different cellular processes. Here, we present a novel, versatile and open accessible program based on Python for simulating molecular membrane diffusion, specifically for three dominant models: Brownian diffusion, compartmentalized diffusion (with transient confinement in larger areas), and trapped diffusion (with transient slowdowns due to interactions). A Voronoi transformation on a uniform random distribution of seed points is performed for compartmentalized and trapping diffusion simulations to construct, respectively, the underlying network of distinct boundaries and random distributed trapping sites. We simulate signals obtained for different fluorescence microscopy measurement modes such as single-particle tracking and various Fluorescence Correlation Spectroscopy based approaches. Our ultimate goal is to develop a simulation toolbox that enables a better understanding of diffusion dynamic data obtained in living cells.