A Study of Posterior Stability in Time-Series Latent Diffusion

Latent diffusion has achieved remarkable success in image generation, with high sampling efficiency. However, this framework might suffer from posterior collapse when applied to time series. In this work, we first show that latent diffusion with a collapsed posterior degenerates into a much weaker generative model: variational autoencoder (VAE). This finding highlights the significance of addressing the problem. We then introduce a principled method: dependency measures, which quantify the sensitivity of a recurrent decoder to input variables. Through this method, we confirm that posterior collapse seriously affects latent time-series diffusion on real time series. For example, the latent variable has an exponentially decreasing impact on the decoder over time. Building on our theoretical and empirical studies, we finally introduce a new framework: posterior-stable latent diffusion, which interprets the diffusion process as a type of variational inference. In this way, it eliminates the use of risky KL regularization and penalizes decoder insensitivity. Extensive experiments on multiple real time-series datasets show that our new framework is with a highly stable posterior and notably outperforms previous baselines in time series synthesis.