  This paper introduces a new latent variable generative model able to handle
high dimensional longitudinal data and relying on variational inference. The
time dependency between the observations of an input sequence is modelled using
normalizing flows over the associated latent variables. The proposed method can
be used to generate either fully synthetic longitudinal sequences or
trajectories that are conditioned on several data in a sequence and
demonstrates good robustness properties to missing data. We test the model on 6
datasets of different complexity and show that it can achieve better likelihood
estimates than some competitors as well as more reliable missing data
imputation. A code is made available at
\url{https://github.com/clementchadebec/variational_inference_for_longitudinal_data}.
