1. A fluorescence observation apparatus comprising: a processor comprising hardware, wherein the processor is configured to: generate a fluorescence image from fluorescence image information acquired by a fluorescence image sensor capturing fluorescence generated in a subject by radiation of excitation light from a light source to the subject; generate a reference image from reference image information acquired by a reference image sensor capturing reflected light returned from the subject by radiation of illumination light from the light source to the subject; generate a division image by dividing an image based on the fluorescence image by an image based on the reference image; control a display to display a corrected fluorescence image based on the division image; apply correction processing to at least one of the reference image, the fluorescence image, and the division image, wherein the correction processing is applied prior to the generation of the division image or prior to the display of the corrected fluorescence image by the display; determine one or more observation conditions of the subject; set parameters regarding the correction processing according to the one or more observation conditions determined; apply different post-processing under a plurality of post-processing modes to the division image to generate the corrected fluorescence image; and set, as post-correction processing parameters, the parameters regarding at least one of the plurality of post-processing modes according to the one or more observation conditions.