A fast algorithm is developed to retrieve temperature, water vapor, and ozone atmospheric profile from the high spectral resolution Infrared Atmospheric Sounding Interferometer spaceborne instrument. Compression, denoising, and pattern recognition algorithms have been developed in a companion paper <Aires et al., 2002b>. A principal component analysis neural network using this a guess information is developed here to retrieve simultaneously temperature, water vapor and ozone atmospheric profiles. The performance of the resulting fast and accurate inverse model is evaluated with a climatological data set including rare events: temperature is retrieved with an error ≤1 K, and total amount of water vapor has a mean percentage error between 5 and 7%. Atmospheric water vapor layers are retrieved with an error between 10 and 15% most of the time. The statistics of the ozone retrieval are too optimistic due to a lack of representation of ozone variability in our test data set.