Latent Laplace Diffusion for Irregular Multivariate Time Series
For practitioners dealing with irregularly sampled time series, LLapDiff provides a generative framework that avoids distortion from re-gridding and drift from sequential solvers, offering improved long-horizon forecasting and imputation.
LLapDiff models irregular multivariate time series as low-dimensional latent trajectories, enabling long-horizon forecasting without step-by-step integration. It achieves state-of-the-art performance on benchmarks, improving over baselines in long-horizon forecasting and supporting missing-value imputation.
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.