Latent Laplace Diffusion Model for Irregular Time Series Forecasting

A new generative framework named Latent Laplace Diffusion (LLapDiff) has been introduced by researchers for forecasting irregular multivariate time series over extended horizons. This approach represents the target as a low-dimensional latent trajectory, facilitating generation across the entire horizon without the need for incremental integration. The reverse process employs a stable modal parameterization derived from stochastic port-Hamiltonian dynamics, with mean evolution defined through learnable complex-conjugate poles in the Laplace domain for direct assessment at irregular timestamps. A renewal-averaging analysis connects continuous dynamics with irregular observations, associating sampling gaps with effective event-domain poles and inspiring a gap-aware history summarizer. This method tackles the challenges posed by discrete techniques that alter temporal structure and continuous-time models that may drift. The research can be found on arXiv under ID 2605.19805.