Socioeconomic segregation has an important role in the emergence of large-scale inequalities in urban areas. Most of the available measures of spatial segregation depend on the scale and size of the system under study neglect large-scale spatial correlations, or rely on ad-hoc parameters, making it hard to compare different systems on equal grounds. In this talk, I will show a family of non-parametric measures for spatial distributions, based on the statistics of the trajectories of random walks on graphs associated with a spatial system. These diffusion-based quantities provide a consistent estimation of segregation in synthetic spatial patterns, and they were used to analyze the ethnic segregation of metropolitan areas in the US and the UK. They also used to understand the disproportionate incident of COVID-19 cases among African Americans. This approach, as measured through diffusion on graphs, allows us to quantify and compare sociospatial phenomena in urban areas having different sizes, shapes, or peculiar microscopic characteristics.