Word meanings change over time and an automated procedure for extracting this information from text would be useful for historical exploratory studies, information retrieval or question answering. We present a dynamic Bayesian model of diachronic meaning change, which infers temporal word representations as a set of senses and their prevalence. Unlike previous work, we explicitly model language change as a smooth, gradual process. We experimentally show that this modeling decision is beneficial: our model performs competitively on meaning change detection tasks whilst inducing discernible word senses and their development over time. Application of our model to the SemEval-2015 temporal classification benchmark datasets further reveals that it performs on par with highly optimized task-specific systems.