What's the purpose of a diode across capacitor after voltage regulator?
Those two diodes perform a useful function when the external load is connected between the power supply outputs (this configuration doubles the voltage potential of the positive rail).

In this case, if the load becomes short circuit then the two outputs will fight each other, one will become dominant and in this situation the diodes prevent one of the outputs (Capacitors) becoming reverse biased.

In addition, at power supply switch on, one of the rails will "come up" faster than the other one and in this situation the diodes prevent the "slow to rise rail" becoming reverse biased. I think the same situation can occur at power down.

To summarise, the diodes are reverse bias protection.

These two diodes should be rated for the full output current of the power supply.