Photoacoustics Imaging is an emerging imaging modality enabling the recovery of functional tissue parameters such as blood oxygenation. However, quantifying these still remains challenging mainly due to the non-linear influence of the light fluence which makes the underlying inverse problem ill-posed. We tackle this gap with invertible neural networks and present a novel approach to quantifying uncertainties related to reconstructing physiological parameters, such as oxygenation. According to in silico experiments, blood oxygenation prediction with invertible neural networks combined with an interactive visualization could serve as a powerful method to investigate the effect of spectral coloring on blood oxygenation prediction tasks.