The vertical distribution of atmospheric ice impacts Earth's weather and climate. The Ice Cloud Imager (ICI) will measure at microwave and sub-millimetre frequencies, which are well suited to detect atmospheric ice. In this study, a machine learning model is trained on ICI simulations. Results show that the vertical distribution of ice can be derived from ICI observations, and that ICI could offer a valuable data source that complements existing radar- and lidar-based measurements.