Some source says the problems began due to turbulence. Perhaps severe turbulence damaged fuel lines and the leak caught fire?
It came down in two minutes after S.O.S and the plane was flying above 30k ft, which could be an indication of a very bad fire onboard the plane. The engines are on the fuselage, so if a fuel line ruptured near the engine, it could have severed all control lines in the aft section of the plane, caused inability to pitch the plane and made it impossible for pilots to pull out from a dive. Either ways, they came down with a descent rate of more than 10,000ft per minute, which is way too steep.