  This paper focuses on the analysis of sequential image data, particularly
brain imaging data such as MRI, fMRI, CT, with the motivation of understanding
the brain aging process and neurodegenerative diseases. To achieve this goal,
we investigate image generation in a time series context. Specifically, we
formulate a min-max problem derived from the $f$-divergence between neighboring
pairs to learn a time series generator in a nonparametric manner. The generator
enables us to generate future images by transforming prior lag-k observations
and a random vector from a reference distribution. With a deep neural network
learned generator, we prove that the joint distribution of the generated
sequence converges to the latent truth under a Markov and a conditional
invariance condition. Furthermore, we extend our generation mechanism to a
panel data scenario to accommodate multiple samples. The effectiveness of our
mechanism is evaluated by generating real brain MRI sequences from the
Alzheimer's Disease Neuroimaging Initiative. These generated image sequences
can be used as data augmentation to enhance the performance of further
downstream tasks, such as Alzheimer's disease detection.
