IL-DiffTSF: Invertible Latent Diffusion for Probabilistic Time Series Forecasting

Internet of Things (IoT) devices generate large volumes of time series data that are often volatile and complex, making probabilistic time series forecasting (TSF) essential for modeling the distribution of future outcomes. Recently, diffusion-based TSF methods have gained attention for their ability to learn complex distributions. However, they typically apply the diffusion process directly in the time domain, which may struggle to capture complex temporal dependencies, thus limiting the full potential of the diffusion process. Besides, they obtain probabilistic forecasts by sampling multiple plausible outcomes from the learned distribution, which is time-consuming and less effective. To solve these problems, we propose invertible latent diffusion for probabilistic time series forecasting (IL-DiffTSF), a novel approach based on a latent diffusion model. Specifically, we design an invertible latent projection (ILP) between time series and latent space, where a conditional diffusion process is applied. This design ensures bidirectional consistency and minimal information loss, enabling more accurate TSF. Moreover, instead of sampling-based probabilistic forecasting, IL-DiffTSF represents uncertainties by directly learning a mapping from latent representations to prediction errors, achieving faster and more reliable uncertainty estimates. Experiments on univariate and multivariate benchmarks validate the efficiency and effectiveness of IL-DiffTSF. The code for this project is available at https://github.com/vanerkz/IL-DiffTSF