In randomized experiments, interactions between units might generate a treatment diffusion process. For instance, if the intervention is an information campaign realized through a video, some treated units might share the treatment with their friends. Such a phenomenon causes a mis-allocation of individuals in the two treatment arms. This circumstance in turn might introduce a bias in the estimation of the causal effect of the intervention. Inspired by a field experiment on the effect of different types of school incentives aimed at encouraging students to attend cultural events, we present a novel approach to deal with a hidden diffusion process, in the presence of a partially unknown network structure. We address the issue of a partially unobserved network by imputing the presence of missing ties. Then, we develop a simulation-based sensitivity analysis that assesses the robustness of the estimates against the possible presence of a treatment diffusion. We simulate several diffusion scenarios within a plausible range of sensitivity parameters and we compare the treatment effect which is estimated in each scenario with the one that is obtained while ignoring the diffusion process.