In high-resolution scanning microscopy, a sample is excited by illumination radiation to emit fluorescence radiation in such a way that the illumination radiation is focused at a point in or on the sample to form a diffraction-limited illumination spot. The point is imaged in a diffraction-limited manner into a diffraction image on a spatially resolving surface detector, wherein the surface detector has a spatial resolution that resolves a structure of the diffraction image. The sample is scanned by means of different scanning positions with an increment of less than half the diameter of the illumination spot. An image of the sample is generated from the data of the surface detector and from the scanning positions assigned to said data, said image having a resolution that is increased beyond a resolution limit for imaging. For the purposes of distinguishing between at least two predetermined wavelength regions in the fluorescence radiation from the sample, a corresponding number of diffraction structures are generated on the surface detector for the at least two predetermined wavelength ranges, said diffraction structures differing but having a common center of symmetry. The diffraction structures are evaluated when generating the image of the sample.