In this paper we advocate the use of diffusion processes guided by density to perform soft clustering tasks. Our approach interpolates between classical mode seeking and spectral clustering, being parametrized by a temperature parameter β > 0 controlling the amount of random motion added to the gradient ascent. In practice we simulate the diffusion process in the continuous domain by random walks in neighborhood graphs built on the input data. We prove the convergence of this scheme under mild sampling conditions, and we derive guarantees for the clustering obtained in terms of the cluster membership distributions. Our theoretical results are cooroborated by preliminary experiments on man-ufactured data and on real data.