Piston pump device for transfer between a first chamber called the inlet chamber, and a second chamber called the exhaust chamber, comprising: - a tubular sleeve comprising a first orifice called the inlet orifice in fluid communication with the inlet chamber, and a second orifice called the exhaust orifice in fluid communication with the exhaust chamber, the inlet orifice and the exhaust orifice being offset longitudinally along the axis of the tubular sleeve, delimiting a third chamber called the compression chamber between them; - a first piston called the inlet piston, sliding in the tubular sleeve between an extreme open position in which it at least partially exposes the inlet orifice in the sleeve and an extreme closed position in which it closes off the inlet orifice while at least partially leaving the exhaust orifice exposed; - a second piston called the exhaust piston, sliding in the tubular sleeve between an extreme closed position in which it closes off the exhaust orifice while leaving the inlet orifice exposed, and an extreme open position in which it at least partially exposes the exhaust orifice; device in which the inlet piston and the exhaust piston are mechanically independent characterized in that the inlet piston and the exhaust piston are each fitted with sealing rings around their periphery in contact with the internal surface of the sleeve as the pistons (3, 4) slide, in that said exhaust chamber is pressurised at a greater pressure than the pressure in the inlet chamber, and in that movements of the exhaust piston and inlet piston are such that the exhaust piston is held in its extreme position closing the exhaust orifice until the inlet piston reaches a first intermediate closed position in which it closes off the inlet orifice and jointly with the inlet piston delimits a volume of the compression chamber such that the gas pressure inside it is at least equal to the gas pressure in the exhaust chamber, sliding of the exhaust piston from its extreme closed position to its open position allowing compressed gas to pass into the exhaust chamber. - a tubular sleeve comprising a first orifice called the inlet orifice in fluid communication with the inlet chamber, and a second orifice called the exhaust orifice in fluid communication with the exhaust chamber, the inlet orifice and the exhaust orifice being offset longitudinally along the axis of the tubular sleeve, delimiting a third chamber called the compression chamber between them; - a first piston called the inlet piston, sliding in the tubular sleeve between an extreme open position in which it at least partially exposes the inlet orifice in the sleeve and an extreme closed position in which it closes off the inlet orifice while at least partially leaving the exhaust orifice exposed; - a second piston called the exhaust piston, sliding in the tubular sleeve between an extreme closed position in which it closes off the exhaust orifice while leaving the inlet orifice exposed, and an extreme open position in which it at least partially exposes the exhaust orifice; device in which the inlet piston and the exhaust piston are mechanically independent characterized in that the inlet piston and the exhaust piston are each fitted with sealing rings around their periphery in contact with the internal surface of the sleeve as the pistons (3, 4) slide, in that said exhaust chamber is pressurised at a greater pressure than the pressure in the inlet chamber, and in that movements of the exhaust piston and inlet piston are such that the exhaust piston is held in its extreme position closing the exhaust orifice until the inlet piston reaches a first intermediate closed position in which it closes off the inlet orifice and jointly with the inlet piston delimits a volume of the compression chamber such that the gas pressure inside it is at least equal to the gas pressure in the exhaust chamber, sliding of the exhaust piston from its extreme closed position to its open position allowing compressed gas to pass into the exhaust chamber.