  We propose a new concept of lifts of reversible diffusion processes and show
that various well-known non-reversible Markov processes arising in applications
are lifts in this sense of simple reversible diffusions. Furthermore, we
introduce a concept of non-asymptotic relaxation times and show that these can
at most be reduced by a square root through lifting, generalising a related
result in discrete time. Finally, we demonstrate how the recently developed
approach to quantitative hypocoercivity based on space-time Poincar\'e
inequalities can be rephrased and simplified in the language of lifts and how
it can be applied to find optimal lifts.
