Latent Laplace Diffusion for Irregular Multivariate Time Series

Irregular multivariate time series pose a fundamental trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often rely on sequential numerical solvers that are prone to drift. To bridge this gap, we present the 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 using a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, allowing for direct evaluation over irregular timestamps. Moreover, we link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and theoretically motivates a gap-aware history summarizer for conditioning. Extensive experiments demonstrate that LLapDiff consistently outperforms baselines in long-horizon forecasting, and its continuous-time generative nature also supports missing-value imputation by querying the same model at historical timestamps.