How can the circuits D1 and D2 in the figure realize the function of preventing short circuit?

D1 is to prevent the input short circuit, VO backflow damage LMX17, D2 is to prevent VO short circuit C2 discharge damage LMX17 only! It is not to prevent input or output short circuit.

My understanding is that D2 prevents the output short circuit and discharges the energy stored in C2, so that lm317 has no output, thus playing the role of output short circuit protection. This is ti's official manual, D1 D2 function description can not be wrong.

When there is no D1, the input is short-circuited, and when V0 is still there, it will damage the LM317. When there is D1, it will pass the diode circuit.

Similarly, when the output is short-circuited, the capacitor c2 passes through the D2 circuit.