In a process for the separation of a stream containing carbon dioxide, water and at least one light impurity including a separation step at subambient temperature, the feed stream (1,3) is compressed in a compressor (C1, C2, C3) comprising at least two stages to form a compressed feed stream (7), the compressed feed stream is purified in an adsorption unit (A1,A2) to remove water and form a dried compressed stream (9, 11), the dried compressed stream or a stream derived therefrom is cooled to a subambient temperature and separated by partial condensation and/or distillation in a separation apparatus (19, 31), liquid enriched in carbon dioxide (37, 43) is removed from the separation apparatus, the adsorption unit is regenerated using a regeneration gas (25, 53) and the regeneration gas is formed by separating, by permeation in a permeation unit (21, 51), the dried compressed stream (9) or a gas (19) derived therefrom, the permeate of the permeation unit constituting the regeneration gas.