Downfall vs. Doom

It ironically appears that GRRM heavily based his Doom of Valyria and related events upon Tolkien's Downfall of Númenor. 

The Downfall of Numenor

The Númenóreans were the strongest and proudest race of humans who ruled a vast overseas empire from their island home, they themselves having distinct physical features that set them apart from other humans (great height). Then, to cut a long story short, they fell from their wisdom and embarked on a deed that promised destruction. But before they fell, Amandil son of Númendil, Lord of Andúnië led his people away and so escaped the utter and complete rupturing and flooding that followed which coupled with the total annihilation of Númenor. His son Elendil would go on to found the Kingdoms of Gondor and Arnor in Middle-Earth.

The Doom of Valyria

In GRRM's A Song of Ice and Fire universe, Valyria was the
strongest and proudest of civilizations, ruling a vast overseas empire from their peninsula  home, they themselves having distinct physical features that set them apart from other humans (purple eyes and silver-gold hair). Exactly how and why they fell remains a mystery, but before the Doom occurred, the daughter of Lord Aenar Targaryen had visions of a cataclysm that would overcome Valyria. A foresight which came true as the Valyrian Peninsula was flooded and shattered beyond repair. Thus he fled to Westeros, where his descendant Aegon the Conqueror would unite the land under the Iron Throne.

Thus in both cases did a noble House flee the vast empire before it's destruction and would go on to be Kings and lords of humans. Of course, Númenor as well as Gondor and Arnor are vastly more noble and humane realms than Old Valyria and Westeros, but the fact still remains.