Particle approximation of diffusion I will present recent work on deterministic particle methods for a wide range of diffusion equations, including the heat equation, the porous medium equation, fast diffusion equations, and height constrained transport. The main idea is to introduce a nonlocal version of the relevant equation and prove that solutions of the nonlocal equation converge to those of the original PDE. In this talk, I will highlight the how the convergence arguments take advantage of the gradient flow structures of the PDEs under consideration. Based on joint work with Katy Craig and Matt Jacobs.