Diffusion network inference and meme tracking have been two key challenges in viral diffusion. This paper shows that these two tasks can be addressed simultaneously with a probabilistic model involving a mixture of mutually exciting point processes. A fast learning algorithms is developed based on mean-field variational inference with budgeted diffusion bandwidth. The model is demonstrated with applications to the diffusion of viral texts in (1) online social networks (e.g., Twitter) and (2) the blogosphere on the Web.