A probabilistic data analysis method was applied to analyze the spatially resolved beam emission intensities from the lithium beam diagnostic at ASDEX Upgrade. The method allows us to recover density profiles from the Li I emission profile with a spatial resolution of 5 mm and a temporal resolution of 50 µs. It is based on a probabilistic description of the measured data including absolutely calibrated measurement errors, a forward model for the simulation of the data given a density profile, and prior information about weak constraints on monotonicity. The density profile is parametrized by cubic spline polynomials. The method replaces the conventional approach applying an iterative (shooting) method to invert the density profile. The new probabilistic method allows us to analyze low-density profiles since there is no need to fulfil an inner boundary condition or to pre-smooth measured data because no direct inversion occurs. Consistent profile uncertainty measures are provided for different purposes. Profiles in the edge region can be fully explored for any plasma regime and the profile pedestal is accessible up to 0.8 × 10²⁰ m⁻³. The advanced technique is demonstrated with low, medium and high density profiles at ASDEX Upgrade. The benefit of the achieved temporal resolution is shown with ELM resolved measurements. The dependence of the density profiles on electron temperature or impurity content is shown to be negligible.