用拉普拉斯域建模不规则多变量时间序列，实现长程预测与缺失值补全。
Latent Laplace Diffusion for Irregular Multivariate Time Series
- 在拉普拉斯域用可学习共轭极点建模潜空间轨迹，跳过逐步积分。
- 长时序预测性能超越基线模型，支持任意时间点直接采样。
- 适合处理不规则采样数据，尤其适用于医疗、金融等缺失值场景。
不规则多变量时间序列在长程预测中面临权衡：离散方法因重采样扭曲时间结构，连续模型则依赖易产生漂移的顺序求解器。为此，我们提出潜空间拉普拉斯扩散（LLapDiff），将目标建模为低维潜轨迹，实现无需逐时步积分的全域生成。通过基于随机端口-哈密顿动力学的稳定模态参数化引导反向过程，并在拉普拉斯域以可学习共轭极点参数化均值演化，支持对不规则时间戳的直接评估。同时，通过更新平均分析将连续动态与不规则观测关联，将采样间隔映射为有效事件域极点，启发设计了考虑时间间隙的历史摘要器。大量实验表明，LLapDiff在长程预测上优于基线，其连续生成特性还支持通过历史时间戳查询完成缺失值补全。代码已公开于 https://github.com/pixelhero98/LLapDiffusion。
原文摘要 · Abstract (English)
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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