This study is focused on the stability and determinants of the Chinese Yuan (CNY) against the U.S. dollar exchange rate movement. To this end, a distribution dynamics model is introduced. We establish the non-linearity of the Generalized normal (GEN) distribution and estimate the impact of macroeconomic variables, such as interest rates, on exchange rate dynamic conditional probability density functions (PDFs). As the distribution allows for fluctuations in the exchange rate, the conditional probability density function (PDF) reveals a time-varying multimodality (i.e., unimodality and bimodality), based on the change in the shape parameters of the generalized normal (GEN) distribution. A unimodal distribution corresponds to a stable equilibrium for exchange rate movement. In contrast, a bimodal distribution contains an unstable equilibrium. Moreover, the bimodality may offer insights into the exchange rate fluctuations resulting from foreign exchange crises or global financial crises. In contrast with previous research on the linearity between macroeconomic variables and exchange rate movements, this study presents novel evidence on the dynamic non-linearity distribution of CNY exchange rate movements and their determinants. Our empirical analysis results will serve as a reference point for macroeconomic policymakers.