Open the stm32f4 datasheet and search for table 15
"Table 15. Limitations depending on the operating power supply range"
The MCU can work with 1.8V power supply with some limitations :
ADC: 1.2Msps
fFlashMax = 20MHz
max flash frequency = 160Mhz / 7 wait states
I/O: decreased performance, no I/O compensation
clock output on I/O pins frequency: <30MHz
flash memory operations: 8bit only
I guess that if you replace the 3.3V regulators on the discovery board with 1.8V regulators you will have a 1.8V discovery board with some performance limitations.