The invention relates to a method for assembling titanium parts and steel parts by diffusion welding that comprises placing two thin spacers (14, 16) made of niobium or vanadium and of copper, respectively, between a titanium part (10) and a steel part (12), placing the part and spacer assembly under vacuum, and subjecting the same to hot isostatic compression at a temperature of between 900 DEG C and 950 DEG C and under a pressure of between 1000 and 1500 bars for about two hours. The invention also relates to the production of turbine shafts for turbine engines.