Human trajectory forecasting is important for intelligent multimedia systems operating in visually complex environments, such as autonomous driving and crowd surveillance. Although Conditional Flow Matching (CFM) has shown strong ability in modeling trajectory distributions from spatio-temporal observations, existing approaches still focus primarily on supervised fitting, which may leave social norms and scene constraints insufficiently reflected in generated trajectories. To address this issue, we propose TIGFlow-GRPO, a two-stage generative approach that aligns flow-based trajectory generation with behavioral rules. In the first stage, we build a CFM-based predictor with a Trajectory-Interaction-Graph (TIG) module to model fine-grained visual-spatial interactions and strengthen context encoding. This stage captures both agent-agent and agent-scene relations more effectively, providing more informative conditional features for subsequent alignment. In the second stage, we perform Flow-GRPO post-training, where deterministic flow rollout is reformulated as stochastic ODE-to-SDE sampling to enable trajectory exploration, and a composite reward combines view-aware social compliance with map-aware physical feasibility. By evaluating trajectories explored through SDE rollout, GRPO progressively steers multimodal predictions toward behaviorally plausible futures. Experiments on the ETH/UCY and SDD datasets show that TIGFlow-GRPOimproves forecasting accuracy and long-horizon stability while generatingtrajectories that are more socially compliant and physically feasible.These results suggest that the proposed approach provides an effective way to connectflow-based trajectory modeling with behavior-aware alignment in dynamic multimedia environments.
Figures & tables
Figure 1. Representative examples of social interaction patterns and scene semantics. From left to right, the teaser shows group separation, individual motion direction, accompany and convergence behaviors, and semantic scene regions with different safety states, including no-entry, hazardous, and safe areas. Top-view pedestrian scene examples illustrating representative interaction patterns, including group separation, individual motion direction, accompany and convergence behaviors, together with semantic regions labeled as no-entry, hazardous, and safe.
Figure 2. Overview of TIGFlow-GRPO. A spatio-temporal encoder produces context tokens from historical trajectories and interaction context, the flow-matching backbone generates future trajectories through ODE rollout, and Flow-GRPO post-training further aligns the predictions with social and physical constraints. A left-to-right diagram of the TIGFlow-GRPO method. Historical trajectories and interaction context are encoded into context tokens, which are used by a flow-matching backbone to generate future trajectories through ODE rollout. A Flow-GRPO post-training module then aligns the predictions with social and physical constraints using stochastic rollout, reward computation, advantage estimation, and a frozen reference branch.
Figure 3. Flow-GRPO reward modeling and policy optimization. Predicted trajectories are organized into G completions and combined with environment features extracted from scene data. A visibility-constraint reward model and an obstacle-avoidance reward model evaluate each completion, and their outputs are aggregated for GRPO optimization. A pipeline diagram of the Flow-GRPO module. Predicted trajectories enter from the left, while scene data are processed by an environment feature extractor. The resulting group of completions contains trajectory states, trajectory features, physical interaction features, and scene features. These completions are evaluated by a visibility-constraint reward model and an obstacle-avoidance reward model, whose outputs are combined and passed to GRPO.
Datasets
GroupNet ( Xu et al., 2022a )
MID ( Gu et al., 2022 )
EqMotion ( Xu et al., 2023 )
EigenTraj ( Bae et al., 2023 )
LED ( Mao et al., 2023 )
SingularTraj ( Bae et al., 2024 )
MoFlow ( Fu et al., 2025 )
DD-MDN ( Hetzel et al., 2026 )
TIGFlow-GRPO Ours
ETH
0.46/0.73
0.39/0.66
0.40/0.62
0.37 / 0.54
0.39/0.58
0.35 / 0.43
0.40/0.60
0.35 / 0.54
0.39/ 0.55
HOTEL
0.15/0.25
0.13/0.22
0.11 /0.18
0.13/0.19
0.11 / 0.17
0.13/0.20
0.12 /0.18
0.13/0.18
0.11 / 0.16
UNIV
0.26/0.49
0.22 /0.45
0.23 /0.42
0.24/0.40
0.26/0.44
0.26/0.45
0.23 /0.40
0.24/0.42
0.22 / 0.38
ZARA1
0.21/0.39
0.17 /0.30
0.18/0.34
0.19/0.33
0.18/ 0.26
0.19/0.33
0.17 /0.29
0.17 / 0.28
0.16 / 0.26
ZARA2
0.17/0.33
0.13 /0.27
0.13 /0.25
0.14/0.24
0.13 / 0.22
0.15/0.26
0.13 / 0.22
0.12 / 0.21
0.12 / 0.21
AVG
0.25/0.44
0.21 /0.38
0.22/0.36
0.21 /0.34
0.21 /0.33
0.22/0.33
0.21 /0.34
0.20 / 0.32
0.20 / 0.31
Table 1. Quantitative comparison of best-of- K ADE min / FDE min on the ETH/UCY benchmark, where the minimum error is reported over K predicted trajectories. Bold and underlined entries denote the best and second-best results, respectively. Lower values indicate better forecasting accuracy, and TIGFlow-GRPO achieves the best overall performance.
Method
ADE
FDE
SocialGAN ( Gupta et al., 2018 )
27.23
41.44
Y-net ( Mangalam et al., 2021 )
11.51
20.24
GroupNet ( Xu et al., 2022a )
9.31
16.11
MID ( Gu et al., 2022 )
9.73
15.32
EigenTraj ( Bae et al., 2023 )
8.05
13.25
LED ( Mao et al., 2023 )
8.49
12.67
Table 2. Quantitative comparison of best-of- K ADE min and FDE min on the Stanford Drone Dataset (SDD), reported in pixels. Bold and underlined entries denote the best and second-best results, respectively.
ETH
MoFlow ( Fu et al., 2025 )
TIGFlow-GRPO
Time
ADE avg
FDE avg
ADE avg
FDE avg
1.2s
0.33
0.52
0.29
0.46
2.4s
0.66
1.25
0.59
1.11
3.6s
1.05
2.15
0.94
1.93
4.8s
1.49
3.10
1.30
2.72
Table 3. Performance degradation over extended prediction horizons exemplified on ETH, measured by ADE avg and FDE avg . TIGFlow-GRPO consistently outperforms the MoFlow baseline across all time steps.
Method
Horizon
ETH
HOTEL
UNIV
ZARA1
ZARA2
SDD
MoFlow ( Fu et al., 2025 )
1.2s
0.55
2.83
5.72
1.14
2.63
1.92
2.4s
3.55
4.74
13.23
3.64
8.12
12.62
3.6s
4.92
7.81
15.92
7.94
13.26
15.85
4.8s
5.63
9.63
19.65
11.63
16.54
19.74
TIGFlow-GRPO
1.2s
0.61
1.35
4.34
0.43
1.58
0.83
2.4s
2.95
2.67
11.04
2.93
6.57
9.45
Table 4. Collision rates (%) across datasets and horizons. TIGFlow-GRPO demonstrates superior collision avoidance in most settings.
Figure 4. Qualitative results on the ETH/UCY benchmark. Compared with DD-MDN, TIGFlow-GRPO produces predictions that better follow local interaction patterns and feasible motion paths across ETH, HOTEL, UNIV, ZARA1, and ZARA2. A 3-by-5 grid of bird's-eye-view trajectory prediction examples from the ETH/UCY benchmark, with columns corresponding to ETH, HOTEL, UNIV, ZARA1, and ZARA2. Purple lines denote observed past trajectories, red lines denote ground-truth futures, yellow lines denote DD-MDN predictions, and orange lines denote TIGFlow-GRPO predictions. In crowded scenes such as UNIV and ZARA1, TIGFlow-GRPO produces more interaction-consistent futures. In structured scenes such as ETH and HOTEL, its predictions better follow feasible walking regions and scene boundaries.
Model Variant
ETH
ADE min
FDE min
ADE avg
FDE avg
w/o TIG-GAT
0.404
0.593
1.494
3.103
w/o social reward
0.401
0.581
1.316
2.745
w/o map reward
0.398
0.577
1.301
2.719
w/o GRPO
0.394
0.555
1.328
2.855
Ours (Full)
0.391
0.553
1.300
2.718
Table 5. Ablation study exemplified on the ETH dataset. Bold values indicate the best performance. The removal of any core component noticeably degrades performance.
Trajectory prediction methods have demonstrated remarkable capabilities in capturing complex motion patterns. However, existing methods rely on global state assumptions, suffer from insufficient belief inference under partial observability, and lack cognitive behavioral constraints in prediction. These limitations severely compromise both deployment feasibility and physical plausibility in real-world settings. In this work, we propose FEP-Diff, an agent-centric trajectory prediction framework grounded in the Free Energy Principle, aimed at achieving cognitively plausible predictions under realistic constraints. Specifically, a dual-branch spatiotemporal encoder extracts ego-motion dynamics and social interaction cues from local observations. Building upon this, a goal-conditioned belief learner infers multimodal latent belief distributions optimized via a free-energy objective, with a social consistency constraint on the local neighborhood graph to promote cognitive alignment among neighboring agents. Finally, a residual diffusion trajectory generator is conditioned on the learned belief representations with token-level proxy conditioning, producing precise and diverse future predictions. Extensive experiments on five public benchmarks demonstrate that FEP-Diff consistently outperforms state-of-the-art methods under restricted observability. Code: https://anonymous.4open.science/r/FEP-Diff-8876.
Yanping Wu, Ji Zhang, Hao Chen +2
University of Glasgow Glasgow, UK · Southwest Jiaotong University Chengdu, China
Human trajectory forecasting is crucial for safe navigation in crowded environments, requiring models that balance accuracy with computational efficiency. Efficiently modeling social interactions is key to performance in dense crowds. Yet, most recent methods rely on attention mechanisms, which are effective at capturing complex dependencies, but incur quadratic computational costs that scale poorly with the growing number of neighbors. Recently, Selective State-Space Models have provided a linear-time alternative; however, their inherently sequential design is misaligned with the unstructured and dynamic nature of social interactions. To address this challenge, we propose Social-Mamba, a forecasting architecture that reformulates social interactions as structured sequential processes. At its core is the Cycle Mamba block, a novel module that enables continuous bidirectional information flow. Social-Mamba organizes agents on an egocentric grid and introduces social triplet factorization, which decomposes interactions into temporal, egocentric, and goal-centric scans. These are dynamically integrated through a learnable social gate and global scan to generate accurate and efficient trajectory predictions. Extensive experiments on five trajectory forecasting benchmarks show that Social-Mamba achieves state-of-the-art accuracy while offering superior parameter efficiency and computational scalability. Furthermore, embedding Social-Mamba into a flow-matching framework further enhances both accuracy and efficiency, establishing it as a flexible and robust foundation for future trajectory forecasting research. The code is publicly available: https://github.com/vita-epfl/Social-Mamba
Stochastic Human Trajectory Prediction (HTP) using generative modeling has emerged as a significant area of research. Although state-of-the-art models excel in optimizing the accuracy of individual agents, they often struggle to generate predictions that are collectively compliant, leading to output trajectories marred by social collisions and environmental violations, thus rendering them impractical for real-world applications. To bridge this gap, we present JACoP: Joint Alignment for Compliant Multi-Agent Prediction, an innovative multi-stage framework that ensures scene-level plausibility. JACoP incorporates an Anchor-Based Agent-Centric Profiler for effective initial compliance filtering and employs a Markov Random Field (MRF) based aligner to formalize the joint selection for scene predictions. By representing inter-agent spatial and social costs as MRF energy potentials, we successfully infer and sample from the joint trajectory distribution, achieving prediction with optimal scene compliance. Comprehensive experiments show that JACoP not only achieves competitive accuracy, but also sets a new standard in reducing both environmental violations and social collisions, thereby confirming its ability to produce collectively feasible and practically applicable trajectory predictions.
Qingze Liu, Alen Mrdovic, Danrui Li +3
Rutgers University, New Brunswick · The College of New Jersey