We study drift dynamics in high-frequency financial returns using a semiparametric approach based on the conventional semimartingale representation of asset prices. By exploiting the exact discretization of the continuous-time process, our framework allows us to formally test for the presence of stochastic drift dynamics in the data and to assess its impact on the return volatility. The main empirical results we find are the following: (i) there is compelling evidence of intraday drift dynamics in stock returns; (ii)  when the drift moves significantly, our method provides a better measure of volatility compared to traditional estimators neglecting the randomness of the drift process; (iii) drift episodes are persistent over time and can be predicted based on past data; (iv)  the post-pandemic boom in the S&P 500 began earlier than suggested by standard low-frequency bubble detection methods.