Atmospheric quantities such as CO2 concentrations are retrieved by inferring their values from indirect measurements consisting of reflectance intensities in different spectral bands. To date, these retrievals are usually carried out separately for each pixel or spatial location. We propose to carry out spatial retrievals, which solve the retrieval problem simultaneously for multiple neighboring pixels. Spatial retrievals can exploit the fact that atmospheric variables vary smoothly over space, especially at higher altitudes where they are well mixed. Hence, atmospheric properties at nearby pixels are strongly correlated. By translating this correlation structure into a regularization term, spatial smoothness is enforced probabilistically. This essentially allows spatial retrievals to borrow information from measurements at nearby pixels, thereby resulting in more accurate retrievals.