Latent Laplace Diffusion for Irregular Multivariate Time Series

TL;DR

Latent Laplace Diffusion (LLapDiff) is a novel generative framework for irregular multivariate time series that models low-dimensional latent trajectories, enabling accurate long-horizon forecasting and missing-value imputation without step-by-step integration.

Contribution

The paper introduces LLapDiff, a continuous-time generative model using Laplace domain parameterization and modal dynamics, bridging the gap between discrete and continuous-time methods for irregular time series.

Findings

LLapDiff outperforms baselines in long-horizon forecasting.

Supports missing-value imputation by querying at historical timestamps.

Utilizes a gap-aware history summarizer for irregular sampling.

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.