The former Soviet Republics and Warsaw Pact states did greatly benefit from the fall of the Soviet Bloc, at which time they were warmly welcomed into the Western fold, backed by the full power of America's military and economic might. "Corruption" is an intangible which can be hard to measure or even identify, since it can be manifested in any number of ways. At its core, politics is just different factions angling for position, using whatever means are at their disposal to bring about a desired outcome.
As it so happens, at least for the past few centuries or so, the countries of the West enjoyed an upper hand and a distinct advantage in terms of industrial development, the global acquisition of resources and control of trade routes and commerce. For whatever reason, some nations got a head start in that process which clearly gave them a distinct advantage over much of the rest of the world which was left behind or ultimately dominated by the West.
So, it's never been any great secret that the West has been better off, financially, industrially, and militarily than most of the rest of the world for quite some time. Other countries which have been traditional allies of the West or otherwise friendly to Western interests have also benefited from the vast wealth and resources of the West. This would include the aforementioned Baltic States, Romania, and possibly even Ukraine in the future. Being aligned with America and the West comes with certain perks and luxuries that the Soviets couldn't afford to offer. Bad luck for them.
The result is a world where a few fortunate nations have become wealthy, powerful, and with far greater influence and might than the vast majority of nations which are weaker and tend to fall under the hegemony and influence of larger powers. That may be a different form of "corruption" which takes place, but it's also been the reality of how the world has generally worked.
I don't know how that can be changed. I once believed that the world was moving in a more progressive and enlightened direction, but I'm not so sure anymore. And with the overriding issue of climate change getting worse, it suggests a future where factions and countries will be scrambling for resources and whatever they can in a fight for survival. There will be no global cooperation on this issue as the panic starts to rise.
We have to find a way to stop this insanity.