Learning Coupled Continuous-Time Latent Dynamics from Irregular Events

Modeling dynamic dependencies from irregularly sampled event sequences is a fundamental challenge in modern machine learning. In many real-world systems, individual-level states evolve continuously over time while being simultaneously influenced by population-level dynamics. However, existing methods typically model these processes in isolation or rely on discrete-time approximations that fail to capture long-range temporal irregularities and sparse observations. This paper studies the problem of learning coupled continuous-time latent dynamics from irregular events, where individual event sequences and global distributional processes evolve asynchronously and interact over time. We propose a Coupled Continuous-Time Latent Dynamics (CoCLD) framework that jointly models individual latent dynamics and population-level distributional shifts, and aligns them in a continuous-time latent space. CoCLD integrates a Diffusion-based Latent Interpolator with neural ordinary differential equations, enabling principled interpolation, generation, and alignment of latent states across arbitrary time points. We show that the proposed coupling mechanism yields a consistent estimator of continuous-time latent dynamics under sparse and irregular observations. Empirical evaluations show CoCLD effectively captures dynamic dependencies and generalizes across tasks like next-event prediction, mobility trajectory generation, and sequential behavior modeling, indicating that learning coupled continuous-time latent dynamics is a powerful paradigm for irregular event sequence modeling.

Real-world human and system behaviors—such as urban mobility, app check-ins, and online shopping actions—rarely happen at regular, fixed time intervals. These events occur randomly and unevenly over time, making it hard for existing models to accurately capture how individual habits evolve and how collective population trends shape everyone’s choices at the same time. Current methods either simplify time into discrete fixed steps or only focus on individual behaviors alone, ignoring the natural two-way influence between personal preferences and global group patterns. In this work, we develop a new modeling framework to learn continuous evolving patterns from these irregular event records. Our method smoothly fills in missing behavioral states across long gaps between observed events and simultaneously captures how individual behaviors and overall population trends continuously affect each other over time.