Latent Laplace Diffusion for Irregular Multivariate Time Series

2026-05-19

AI Summary

This work addresses the challenges in long-horizon forecasting of irregular multivariate time series, where discrete approaches disrupt temporal structure and continuous models rely on solvers prone to drift. To overcome these limitations, the authors propose the Latent Laplace Diffusion (LLapDiff) framework, which models continuous trajectories in a low-dimensional latent space and generates entire prediction intervals directly in the Laplace domain via diffusion, thereby circumventing stepwise numerical integration. LLapDiff incorporates a stable complex-pole parameterization grounded in stochastic port-Hamiltonian dynamics to capture mean evolution, and establishes a principled link between continuous dynamics and irregular observations through renewal process analysis, enabling the design of a gap-aware history summarizer. The method significantly outperforms existing baselines in long-horizon forecasting and supports missing value imputation at arbitrary historical timestamps within the same unified model.

Abstract

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Problem

• irregular multivariate time series
• long-horizon forecasting
• temporal structure distortion
• continuous-time models
• sequential solvers

Innovation

• Latent Laplace Diffusion
• irregular time series
• continuous-time generative modeling
• Laplace domain parameterization
• renewal-averaging analysis