The film fails from the title to the ridiculous end. The very questionable love story has nothing to do with the Cold War, it could have taken place at any time. The Cold War most likely didn't cause the failure of Pawlikowski's parents' marriage either. The two characters move around Europe as if the Iron Curtain didn't exist.
I was raised and educated in communist Hungary and left the country in 1964 legally with a passport. The reward for my not returning was a "standard" 2 years jail sentence in absentia. Had I returned later most likely would have been jailed, professionally ruined and blessed with a permanent travel ban. During my Viennese years in the 60s regular tourbuses took the western tourists to the Hungarian border to see the Iron Curtain from the "safe" side: this wasn't the Mexican border, my fellow Americans, it was a continuous razor wire fence, mine field with watchtowers, in today's terms "100% migrant proof". The Berlin Wall wall was simply part of it, a bit more visible more infamous.
As for the love story, it is very unlikely that a highly educated, talented musician irresistibly would fall for a Zula like character. The ending is as banal as it could be.
The only positive thing about the movie is the much praised photography. The black and white, the interruptions, the picture format are mannerisms at best.