Dense crowds are challenging scenes for an autonomous mobile robot. Planning in such an interactive environment requires predicting uncertain human intention and reaction to future robot actions. Concerning these capabilities, we propose a probabilistic forecasting model which factorizes the human motion uncertainty as follows: 1) A (conditioned) normalizing flow (CNF) estimates the densities of human goals. 2) We forecast the crowd’s trajectory density towards the goals by autoregressively (AR) inferring the individual social action densities simultaneously for a dynamic number of persons. We extend the underlying Gaussian AR framework with our SocialSampling to counteract collisions during sampling. Based on this, a model-predictive policy that infers about the social influence of a controlled robot on neighboring humans is created. For this, we formulate a novel Social Influence (SI) objective that measures the divergence between a scene prediction conditioned by the robot plan and a scene prediction independent of the robot plan. The experiments with our metrics on real datasets show that the model achieves stateof-the-art accuracy in predicting pedestrian movements and remains collision-free, which is still often neglected in current methods. Furthermore, our evaluations show that robot policy with our SI objective produces safe and proactive behaviors, such as taking evasive action at the right time to avoid conflicts.