Probabilistic cascade models consider information diffusion as an iterative process in which information transits between users of a network. The problem of diffusion modeling then comes down to learning transmission probability distributions, depending on hidden influence relationships between users, in order to discover the main diffusion channels of the network. Various learning models have been proposed in the literature, but we argue that the diffusion mechanisms defined in most of these models are not well-adapted to deal with noisy diffusion events observed from real social networks, where transmissions of content occur between humans. Classical models usually have some difficulties for extracting the main regularities in such real-world settings. In this paper, we propose a relaxed learning process of the well-known Independent Cascade model that, rather than attempting to explain exact timestamps of users' infections, focus on infection probabilities knowing sets of previously infected users. Furthermore, we propose a regularized learning scheme that allows the model to extract more generalizable transmission probabilities from training social data. Experiments show the effectiveness of our proposals, by considering the learned models for real-world prediction tasks.