FlowCloud: Learning Continuous Spatiotemporal Dynamics from Unpaired Sparse Point Cloud Snapshots

Reconstructing unified continuous dynamics from sparse, non-contiguous, and unpaired point cloud snapshots remains a fundamental challenge in spatiotemporal analysis for computer vision and developmental biology. Existing methods, including scene flow and Optimal Transport-based approaches, are limited either by explicit reliance on point-wise correspondences or by cumulative errors from frame-to-frame propagation and temporal discontinuity, and limited ability to model multi-attribute dynamics such as gene expression and population changes. We propose FlowCloud, a variational Neural Ordinary Differential Equation (Neural ODE) generative framework. FlowCloud aggregates information from all observed time points into a joint latent representation that initializes a Neural ODE $z(t)$ enabling continuous spatiotemporal evolution modeling while mitigating propagation-induced errors and preserving temporal consistency. Training is performed without predefined correspondences using a multi-faceted objective with complementary roles: Sinkhorn distance for global distribution alignment, Chamfer distance for local geometric consistency, trajectory regularization to encourage smooth and physically plausible dynamics, and supervised losses for multi-attribute prediction. Experiments on human motion and developmental biology datasets demonstrate improved interpolation accuracy and promising short-term extrapolation performance. By unifying geometry, attributes, and population dynamics within a continuous latent framework, FlowCloud offers a novel and robust solution for continuous dynamic reconstruction from unstructured spatiotemporal observations.

Imagine trying to piece together a complex movie from just a few scattered photos featuring entirely different actors. Biologists face a similarly daunting challenge, as their disconnected "snapshots" of tissues make it incredibly difficult to track how individual cells continuously grow and change. With our AI system, FlowCloud, we are simply taking a modest step toward bridging this gap. Acting more like a humble "assistant director," it tries its best to analyze these sparse, unlinked glimpses and estimate the underlying rules of development to sketch out a continuous "video." While far from a perfect solution, by offering educated guesses on where cells might move and how their genetics could shift, we hope FlowCloud can serve as a helpful starting point for researchers striving to visualize intricate processes like embryonic development or disease progression.