The number of individuals forcibly displaced by conflicts has been rising in the past few decades. However, we know little about the dynamics - magnitude, timing, and persistence - of conflict-induced migration in the short run. We use novel high-frequency data to estimate the dynamic migration response to conflict for the case of the Mexican Revolution (1910-1917), one of the deadliest conflicts in world history. We find that, on average, insurgency events led to a large increase in migration rates of about 60 percent that lasted for a few months: after five months, migration rates reverted back to pre-violence levels. This finding masks substantial heterogeneity in treatment effects, as we find larger and more persistent effects for women and children. We show that violence was the main treatment channel, with variation in the intensity and nature of violence explaining the magnitude and persistence of the migration response. While migration costs, migrant networks, and land ownership moderated the migration response to conflict, we show that these factors affect different aspects of the response.