A process for the manufacture of a DAFD vapor comprising: a. feeding a furan-2,5-dicarboxylic acid ("FDCA") composition to an esterification reaction zone; and b. in the presence of an alcohol compound, conducting an esterification reaction in the esterification reaction zone to react FDCA with said alcohol compound to form a crude diester composition comprising dialkyl furan-2,5-dicarboxylate ("DAFD"), the alcohol compound, 5-(alkoxycarbonyl)furan-2-carboxylic acid (ACFC), alkyl furan-2-carboxylate, and alkyl-5-formylfuran-2-carboxylate (AFFC), and c. separating at least a portion of the alcohol compound from the crude diester composition in a flash zone using a physical separation process to produce: (i) a vapor alcohol composition, comprising said alcohol compound, taken as an overhead stream that is rich in the concentration of alcohol, relative to the alcohol concentration in the crude diester composition feeding the flash zone, and (ii) a first liquid DAFD rich composition, comprising DAFD, ACFC, AFC, and AFFC, that is rich in the total concentration of DAFD relative to the total concentration of DAFD in the crude diester composition feeding the flash zone; and d. separating at least a portion of the DAFD from the first liquid DAFD rich composition in a product recovery zone; wherein the process produces: (i) a purified DAFD vapor composition rich in the concentration of DAFD relative to the concentration of DAFD in the first liquid DAFD rich composition; and (ii) a liquid ACFC composition that is rich in the concentration of ACFC relative to the concentration of ACFC in the first liquid DAFD rich composition; and (iii) a vapor AFC composition comprising AFC that is rich in the concentration of AFC relative to the concentration of AFC in the first liquid DAFD rich composition; and (iv) a second alcohol composition comprising alcohol that is rich in the concentration of alcohol, relative to the first liquid DAFD rich composition. a. feeding a furan-2,5-dicarboxylic acid ("FDCA") composition to an esterification reaction zone; and b. in the presence of an alcohol compound, conducting an esterification reaction in the esterification reaction zone to react FDCA with said alcohol compound to form a crude diester composition comprising dialkyl furan-2,5-dicarboxylate ("DAFD"), the alcohol compound, 5-(alkoxycarbonyl)furan-2-carboxylic acid (ACFC), alkyl furan-2-carboxylate, and alkyl-5-formylfuran-2-carboxylate (AFFC), and c. separating at least a portion of the alcohol compound from the crude diester composition in a flash zone using a physical separation process to produce: (i) a vapor alcohol composition, comprising said alcohol compound, taken as an overhead stream that is rich in the concentration of alcohol, relative to the alcohol concentration in the crude diester composition feeding the flash zone, and (ii) a first liquid DAFD rich composition, comprising DAFD, ACFC, AFC, and AFFC, that is rich in the total concentration of DAFD relative to the total concentration of DAFD in the crude diester composition feeding the flash zone; and (i) a vapor alcohol composition, comprising said alcohol compound, taken as an overhead stream that is rich in the concentration of alcohol, relative to the alcohol concentration in the crude diester composition feeding the flash zone, and (ii) a first liquid DAFD rich composition, comprising DAFD, ACFC, AFC, and AFFC, that is rich in the total concentration of DAFD relative to the total concentration of DAFD in the crude diester composition feeding the flash zone; and d. separating at least a portion of the DAFD from the first liquid DAFD rich composition in a product recovery zone; wherein the process produces: (i) a purified DAFD vapor composition rich in the concentration of DAFD relative to the concentration of DAFD in the first liquid DAFD rich composition; and (ii) a liquid ACFC composition that is rich in the concentration of ACFC relative to the concentration of ACFC in the first liquid DAFD rich composition; and (iii) a vapor AFC composition comprising AFC that is rich in the concentration of AFC relative to the concentration of AFC in the first liquid DAFD rich composition; and (iv) a second alcohol composition comprising alcohol that is rich in the concentration of alcohol, relative to the first liquid DAFD rich composition. (i) a purified DAFD vapor composition rich in the concentration of DAFD relative to the concentration of DAFD in the first liquid DAFD rich composition; and (ii) a liquid ACFC composition that is rich in the concentration of ACFC relative to the concentration of ACFC in the first liquid DAFD rich composition; and (iii) a vapor AFC composition comprising AFC that is rich in the concentration of AFC relative to the concentration of AFC in the first liquid DAFD rich composition; and (iv) a second alcohol composition comprising alcohol that is rich in the concentration of alcohol, relative to the first liquid DAFD rich composition.