Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility pattern, the observed data often consists of only aggregate information. In this work, we present new models that generalize standard diffusion processes to such collective settings. We also present optimization based techniques that can accurately learn the underlying dynamics of the given contagion process, including the hidden network structure, by only observing the time a node becomes active and the associated aggregate information. Empirically, our technique is highly robust and accurately learns network structure with more than 90% recall and precision. Results on real-world flu spread data in the US confirm that our technique can also accurately model infectious disease spread.