FlowMoP: A New Framework for Stochastic Multi-Person Motion Prediction

Multi-person 3D motion prediction has long been dominated by the deterministic paradigm, where each agent outputs only a fixed number of future trajectories. However, in real-world scenarios, the same historical observation may correspond to multiple plausible futures—depending on intent, coordination, and social context. FlowMoP proposes a conditional flow matching framework that jointly generates diverse future motions for multiple agents while modeling both global trajectories and root-relative poses.

From Deterministic to Stochastic Generation: A Paradigm Shift

Existing mainstream methods treat multi-person motion prediction as a deterministic regression problem, outputting a fixed number of future trajectories for each agent. This design ignores the inherent stochasticity of human behavior: the same historical observation may give rise to multiple plausible futures due to differences in individual intent, group coordination, or social norms. The core insight of FlowMoP is to reframe the prediction problem as a conditional generation task, learning the full distribution of future motions through a flow matching framework rather than a single point estimate.

Compared with diffusion models, conditional flow matching offers advantages in training and sampling efficiency while maintaining generation diversity. FlowMoP jointly generates future motions for multiple agents, meaning that interaction consistency among agents is explicitly modeled during the generation process rather than corrected post hoc.

Conditional Flow Matching is a class of generative modeling methods based on continuous normalizing flows (CNFs). Its core idea is to learn a time-dependent velocity field that continuously transforms a simple prior distribution (such as Gaussian noise) along ordinary differential equation trajectories into the target data distribution. Unlike diffusion models, which add and remove noise step by step, flow matching directly regresses the velocity vectors along a conditional probability path, yielding a simpler training objective and requiring fewer sampling steps for generation. The conditional version uses context such as historical observations and neighbor states as conditions, so that the generated distribution changes dynamically with the input. Compared with diffusion models, flow matching typically offers advantages in sampling efficiency and training stability while retaining the ability to generate multimodal distributions, making it well suited to motion prediction tasks that demand both real-time performance and diversity.

Technical Core: B-spline Compression and Dual-Stream Transformer

FlowMoP's architecture contains two key designs. First, B-spline reparameterization compresses the generative state space into low-dimensional control points while enforcing temporal smoothness. This design both reduces the complexity of the generative model and ensures the physical plausibility of output trajectories—human motion does not exhibit abrupt jitter over short time spans.

Second, a dual-stream transformer provides interaction-aware conditioning for each agent. Each agent's prediction is conditioned on the observed neighbor motions, thereby capturing the influence of social interaction on motion. The dual-stream structure separately handles global trajectories and root-relative poses, enabling the model to attend simultaneously to macroscopic displacement and microscopic pose changes.

B-spline reparameterization is a parameterization technique that represents a continuous curve with a small number of control points. Given a set of control points and basis functions, a B-spline can smoothly interpolate an entire trajectory, with its degree determining the continuity of the curve. In generative modeling, sampling directly in a high-dimensional per-frame state space is costly and prone to jitter; after compressing the state into low-dimensional control points, the generative model only needs to predict these control points, which are then decoded by the B-spline into a full trajectory. On one hand, this significantly reduces the dimensionality of the generative space; on the other hand, the B-spline basis functions themselves impose smoothness constraints that suppress high-frequency noise and ensure physically plausible output trajectories. The cost is that expressiveness is limited by the number and degree of control points, potentially underfitting high-frequency motions such as rapid direction changes.

Dual-stream transformer refers to an architecture that employs two parallel attention streams to handle motion representations at different granularities. In human motion prediction, one stream models the global trajectory (e.g., the displacement of the root node in world coordinates), while the other models the root-relative pose (the local rotation and position of each joint relative to the root node). The two streams interact through cross-stream attention or shared conditioning information, so that predictions of macroscopic displacement and microscopic pose mutually constrain each other. The motivation for this decomposition is that global trajectories and local poses differ in statistical properties and temporal scales, and modeling them jointly tends to cause interference; when handled separately, the model can capture long-range spatial displacement while finely characterizing joint motion, and at the same time achieve interaction-aware conditioning among agents via attention mechanisms.

Experimental Results: Distributional Prediction Outperforms Deterministic Baselines

FlowMoP achieves state-of-the-art performance on two standard datasets, CMU-Mocap (UMPM) and 3DPW. You may not have noticed that although FlowMoP outputs a full predictive distribution rather than a single trajectory, it outperforms deterministic baselines on joint position error, pose error, and final displacement error. This result shows that generative modeling does not sacrifice accuracy; rather, it improves overall prediction quality by capturing multimodality.

The research team also established the first motion prediction baseline on the WorldPose dataset. WorldPose is a large-scale professional soccer dataset containing multi-person interaction scenarios. On this dataset, social conditioning was shown to concentrate prediction uncertainty along the directions of interaction constraints—in other words, the model learns in which directions the future is more certain and in which directions there is disagreement.

How Social Conditioning Shapes Uncertainty

A key finding of FlowMoP is that social interaction information not only improves prediction accuracy but also changes the distributional structure of uncertainty. In soccer scenarios, players' movements are bidirectionally constrained by the positions of teammates and opponents, and the uncertainty generated by the model is not uniformly distributed but concentrated along the directions of interaction constraints. This phenomenon provides a new perspective for understanding the sources of uncertainty in multi-person motion prediction: uncertainty is not pure noise but a reflection of the structure of social interaction.

This work also suggests that the evaluation of future motion prediction systems should not focus solely on point error but should also examine the quality and diversity of the generated distribution. For applications such as autonomous driving, crowd simulation, and sports analytics, being able to generate multiple plausible futures is more practically valuable than giving a single "best guess."

Limitations and Outlook

FlowMoP currently still relies on observed neighbor motions as conditions, and its ability to model unobserved agents or sudden interactions remains to be further validated. In addition, B-spline compression, while improving smoothness, may limit the expressiveness of high-frequency motions. Future work could explore more flexible state representations and extend the flow matching framework to online prediction scenarios.

One-line Summary

FlowMoP uses conditional flow matching to jointly generate diverse future motions for multiple people, balancing accuracy and diversity.

Paragraph Summary

FlowMoP proposes a conditional flow matching framework that transforms multi-person 3D motion prediction from deterministic regression into a conditional generation task, jointly generating diverse future motions for multiple agents. Architecturally, it employs B-spline reparameterization to compress the generative state into low-dimensional control points to ensure temporal smoothness, and uses a dual-stream transformer to separately handle global trajectories and root-relative poses, achieving interaction-aware conditional modeling. On CMU-Mocap (UMPM) and 3DPW, FlowMoP outperforms deterministic baselines on joint position error, pose error, and final displacement error, demonstrating that generative modeling does not sacrifice accuracy. It establishes the first motion prediction baseline on the WorldPose soccer dataset and finds that social conditioning can concentrate prediction uncertainty along the directions of interaction constraints. The article also discusses limitations such as reliance on observed neighbors and the limited high-frequency expressiveness of B-splines.