A method of forming polycrystalline diamond includes encapsulating diamond particles, carbon monoxide, and carbon dioxide in a container. The encapsulated diamond particles, carbon monoxide, and carbon dioxide are subjected to a pressure of at least 4.5 GPa and a temperature of at least 1400° C. to form inter-granular bonds between the diamond particles. A cutting element includes polycrystalline diamond material comprising inter-bonded grains of diamond. The polycrystalline diamond material is substantially free of graphitic carbon and metallic compounds. The polycrystalline diamond material exhibits a density of at least about 3.49 g/cm3 and a modulus of at least about 1000 GPa. An earth-boring tool may include such a cutting element secured to a body.