  Latent diffusion has shown promising results in image generation and permits
efficient sampling. However, this framework might suffer from the problem of
posterior collapse when applied to time series. In this paper, we conduct an
impact analysis of this problem. With a theoretical insight, we first explain
that posterior collapse reduces latent diffusion to a VAE, making it less
expressive. Then, we introduce the notion of dependency measures, showing that
the latent variable sampled from the diffusion model loses control of the
generation process in this situation and that latent diffusion exhibits
dependency illusion in the case of shuffled time series. We also analyze the
causes of posterior collapse and introduce a new framework based on this
analysis, which addresses the problem and supports a more expressive prior
distribution. Our experiments on various real-world time-series datasets
demonstrate that our new model maintains a stable posterior and outperforms the
baselines in time series generation.
