Particles in soft-matter systems (such as colloids) tend to have attractive interactions that are very short-ranged compared to their diameters, so traditional theories, that assume the energy landscape is smooth enough, will struggle to capture their dynamics. We propose a new framework to look at such particles, based on taking the limit as the range of the interaction goes to zero. In this limit, the energy landscape is a set of geometrical manifolds, while the dynamics on top of the manifolds are a diffusion process with “sticky” boundary conditions. This framework leads to new methods to compute dynamical quantities, such as transition rates between clusters of colloids, which give predictions agree quantitatively with our experiments. We propose a numerical method to simulate a sticky diffusion, which preliminary investigations suggest could be orders of magnitude faster than typical methods to simulate mesoscale particles.