Title: Latent Laplace Diffusion for Irregular Multivariate Time Series

Abstract:

Long-horizon forecasting of irregular multivariate time series presents a significant challenge, often forcing a compromise between accuracy and temporal fidelity. Discrete approaches tend to distort the underlying temporal structure through re-gridding, whereas continuous-time models frequently rely on sequential solvers that are susceptible to drift. To address these limitations, we introduce Latent Laplace Diffusion (LLapDiff), a novel generative framework that represents the target data as a low-dimensional latent trajectory. This approach facilitates generation across the entire forecasting horizon without the need for step-by-step integration over physical time.

In our method, the reverse process is guided by a stable modal parameterization inspired by stochastic port-Hamiltonian dynamics. We define the mean evolution within the Laplace domain using learnable complex-conjugate poles, which allows for direct evaluation at irregular timestamps. Furthermore, we establish a connection between continuous dynamics and irregular observations via renewal-averaging analysis. This technique maps sampling gaps to effective event-domain poles and informs the design of a gap-aware history summarizer. Our extensive experimental results demonstrate that LLapDiff outperforms existing baselines in long-horizon forecasting tasks. Additionally, its capability as a continuous-time generative model enables missing-value imputation by querying the model at historical time points. The source code is publicly accessible at https://github.com/pixelhero98/LLapDiffusion.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC