Simulation-based ultrasound training can be an essential educational tool. Realistic ultrasound image appearance with typical speckle texture can be modeled as convolution of a point spread function with point scatterers representing tissue microstructure. Such scatterer distribution, however, is in general not known and its estimation for a given tissue type is fundamentally an ill-posed inverse problem. In this paper, we demonstrate a convolutional neural network approach for probabilistic scatterer estimation from observed ultrasound data. We herein propose to impose a known statistical distribution on scatterers and learn the mapping between ultrasound image and distribution parameter map by training a convolutional neural network on synthetic images. In comparison with several existing approaches, we demonstrate in numerical simulations and with in-vivo images that the synthesized images from scatterer representations estimated with our approach closely match the observations with varying acquisition parameters such as compression and rotation of the imaged domain.