Learning Individual Dynamics from Sparse Cross-Sectional Snapshots

2026-05-22

AI Summary

Recovering continuous individual dynamic trajectories from sparse or even single-timepoint cross-sectional data is inherently ill-posed. This work proposes the CADENCE framework, which, for the first time, provides identifiability guarantees for inferring individual evolution trajectories from a single snapshot by anchoring latent dynamics to individual-specific static context. The method integrates bijective probability flow ordinary differential equations (ODEs) to eliminate diffeomorphic ambiguity and introduces a soft mixture-of-experts (SMoE) routing mechanism to model inter-individual heterogeneity, jointly identifying dynamical parameters and routing functions. Experiments on both physical systems and real-world biological datasets demonstrate that CADENCE, trained solely on sparse snapshots, achieves performance comparable to or even surpassing state-of-the-art sequential models that rely on complete trajectory observations.

Abstract

Predicting how a dynamical unit evolves over time - how an individual ages, an epidemic spreads, or a physical system degrades - typically requires dense longitudinal tracking. When only extremely sparse or entirely cross-sectional data is available, inferring individualized, continuous-time trajectories is fundamentally ill-posed. Existing methods force a strict compromise: sequence models (e.g. latent ODEs) require dense longitudinal data, while cross-sectional methods (e.g. optimal transport, flow matching-based) map aggregate populations, losing individual dynamics. In this paper, we demonstrate that this dichotomy can be broken. We introduce CADENCE, a principled probabilistic framework that recovers continuous individual trajectories from isolated snapshots by anchoring latent dynamics to static, individual-level contexts. We provide novel identifiability guarantees for single-timepoint trajectory inference. By combining a score-based spatial encoder (bijective Probability Flow ODE) to eliminate diffeomorphic ambiguities with a Soft Mixture-of-Experts (SMoE) router, we show that individual dynamical parameters and routing function are jointly identifiable. Across a suite of benchmarks spanning physical systems to real-world biological data, CADENCE, trained strictly on extremely sparse snapshots with context structure, matches or exceeds the performance of state-of-the-art sequential models trained on dense, full-trajectory data.

Problem

• individual dynamics
• sparse cross-sectional data
• trajectory inference
• continuous-time modeling
• identifiability

Innovation

• CADENCE
• individual dynamics
• cross-sectional snapshots
• identifiability
• score-based generative modeling