Cultural differences play an important role in shaping migration patterns. The conventional proxies for cross country cultural differences, such as common language; ethnicity; genetic traits; or religion, implicitly assume that cultural proximity between two countries is constant over time and symmetric. This is far from realistic. This paper proposes a gravity model for international migration which explicitly allows for the time varying and asymmetric dimensions of cultural proximity. In accordance with Disdier, Tai, Fontagné, Mayer (Rev World Econ, 145(4):575–595, 2010) we assume that the evolution of bilateral cultural affinity over time is reflected in the intensity of bilateral trade in cultural goods. The empirical framework includes a comprehensive set of high dimensional fixed effects which enable identification of the impact of cultural proximity on migration over and beyond the effect of pre-existing cultural and historical ties. The results are robust across different econometric techniques and suggest that positive changes in cultural relationships over time foster bilateral migration.