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.

翻译：不规则多变量时间序列在长时域预测中面临权衡：离散方法会因重网格化扭曲时间结构，而连续时间模型通常需要易受漂移影响的序列求解器。为弥合这一差距，我们提出潜拉普拉斯扩散（LLapDiff），一种将目标建模为低维潜轨迹的生成框架，无需在物理时间上逐时间步积分即可实现全时域生成。我们利用受随机端口-哈密顿动力学启发的稳定模态参数化引导逆向过程，并在拉普拉斯域中通过可学习的共轭复极点参数化其均值演化，从而支持在不规则时间戳上直接求值。我们还通过更新平均分析将连续动力学与不规则观测相关联，该方法将采样间隔映射为有效事件域极点，并激发了一种感知间隔的历史总结器。大量实验表明，LLapDiff在长时域预测中优于基线方法，其连续时间生成性质支持通过在同一模型的历史时间戳处查询来实现缺失值插补。代码开源：https://github.com/pixelhero98/LLapDiffusion。