  Generative models using neural network have opened a door to large-scale
studies for various application domains, especially for studies that suffer
from lack of real samples to obtain statistically robust inference. Typically,
these generative models would train on existing data to learn the underlying
distribution of the measurements (e.g., images) in latent spaces conditioned on
covariates (e.g., image labels), and generate independent samples that are
identically distributed in the latent space. Such models may work for
cross-sectional studies, however, they are not suitable to generate data for
longitudinal studies that focus on "progressive" behavior in a sequence of
data. In practice, this is a quite common case in various neuroimaging studies
whose goal is to characterize a trajectory of pathologies of a specific disease
even from early stages. This may be too ambitious especially when the sample
size is small (e.g., up to a few hundreds). Motivated from the setup above, we
seek to develop a conditional generative model for longitudinal data generation
by designing an invertable neural network. Inspired by recurrent nature of
longitudinal data, we propose a novel neural network that incorporates
recurrent subnetwork and context gating to include smooth transition in a
sequence of generated data. Our model is validated on a video sequence dataset
and a longitudinal AD dataset with various experimental settings for
qualitative and quantitative evaluations of the generated samples. The results
with the AD dataset captures AD specific group differences with sufficiently
generated longitudinal samples that are consistent with existing literature,
which implies a great potential to be applicable to other disease studies.
