Latent Laplace Diffusion for Irregular Multivariate Time Series

• URL: http://arxiv.org/abs/2605.19805v1
• Date: Tue, 19 May 2026 13:04:53 GMT
• Title: Latent Laplace Diffusion for Irregular Multivariate Time Series
• Abstract summary: We present Latent Laplace Diffusion, a generative framework that models the target as a low-dimensional latent trajectory.<n>LLapDiff enables horizon-wide generation without step-by-step integration over physical time.<n>We also link continuous dynamics to irregular observations through renewal-averaging analysis.
• Score: 16.474933482743513
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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