Origin of Color Report / Artificial Color Identification (7.39)
It is entirely possible for someone to gain the knowledge and expertise and to buy the necessary instruments, in order to analyze and distinguish irradiated and natural-color diamonds. But to start with, a reputable lab such as GIA, is recommended for identification (origin of color report). It is reliable and for resale purposes, very helpful. 
The above image is courtesy of: https://www.gia.edu/analysis-grading-sample-report-colored-diamond?reporttype=colored-diamond-identification-and-origin-report
The above image is courtesy of: https://www.gia.edu/analysis-grading-sample-report-colored-diamond?reporttype=colored-diamond-identification-and-origin-report
Distinguishing irradiated from natural would primarily start with spectroscopy or the use of a spectroscope.
Surface Stains on Irradiated Green Diamonds: Sometimes microscopic examination reveals green, inert, shallow radiation stains on the surface of the diamond, which contrast with the diamond's natural blue fluorescence but often these stains are removed in the polishing process. In current practices treatment using radioactive salts legally is rarely used today, as it can create dangerously radioactive diamonds. Modern artificial irradiation typically uses low-energy electron beams instead.
The above image is courtesy of: https://www.gia.edu/gems-gemology/winter-2021-microworld-radioactive-green-diamond
Spectroscopy: An infrared spectroscope, is the instrument used to detect and record the diamond’s absorption spectrum. The specific absorption lines can allow gemologists to determine the color origin of the diamond in question. If H1b (1,936 nm) and H1c (2,026 nm) are indicated in absorption lines (relating to hydrogen-vacancy defects), it is then concluded that the diamond is irradiated and/or annealed in Type-Ia diamonds. A pressurized liquid nitrogen (LN2) bottle is a necessary laboratory component for analyzing irradiated diamonds. The cryogenic temperatures with LN2 sharpen the visibility of the diagnostic absorption characteristics in a diamond's visible and photo-luminescent spectra to differentiate irradiated and natural colors.
The above illustration is courtesy of: https://www.researchgate.net/figure/FTIR-spectra-of-the-natural-diamond-a-and-annealed-N-H-codoped-diamond-b-Inset_fig8_264624485
The above image is courtesy of: https://www.rivistaitalianadigemmologia.com/en/2025/03/25/fourier-transform-infrared-spectroscopy-ftir-and-its-gemological-applications/#:~:text=The%20use%20of%20FTIR%20in,synthetic%20origin%20of%20the%20diamond.