Diffusion processes on manifolds have played an important role in mathematics, physics, and data science. This work aims to define diffusion processes on stratified spaces, but their lack of a smooth structure makes this challenging and requires a more general framework. Sturm introduced an approach for constructing diffusion processes on metric measure spaces, relying on the theory of Dirichlet forms and their well-established connection to Markov processes. In this talk, I will discuss how to construct diffusion processes on a class of stratified spaces—subanalytic sets—using Sturm’s approach and tools from geometric measure theory. This is a work in progress.