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, which is far from realistic. This paper proposes a tractable model for international migration which explicitly allows for the time varying and asymmetric dimensions of cultural proximity. Similarly to Disdier et al (2010) we assume that the evolution of bilateral cultural affinity over time is reflected in the intensity of bilateral trade in cultural goods. Our empirical framework includes a comprehensive set of high dimensional fixed effects which enables for the 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.