TrajFlow: Nationwide Pseudo GPS Trajectory Generation with Flow Matching Models¶

Conference: ICLR 2026
OpenReview: https://openreview.net/forum?id=BDOldEjwCE
Code: https://github.com/ZeroCSIS/TrajFlow
Area: Time Series / Spatiotemporal Data / Trajectory Generation / Flow Matching Generative Models
Keywords: Pseudo GPS Trajectory Generation, Flow Matching, Multi-scale, Trajectory Normalization, OD Condition

TL;DR¶

TrajFlow introduces Flow Matching to GPS trajectory generation for the first time. Combined with a "per-trajectory normalization + RDP compression + OD condition normalization" strategy, it stably generates pseudo GPS trajectories across city, metropolitan, and national scales using approximately 10 ODE integration steps. It outperforms diffusion and other deep generative baselines on a dataset covering millions of real trajectories in Japan, showing significant advantages at the national scale.

Background & Motivation¶

Background: Mobile GPS trajectory data is crucial for urban research, pandemic control, and transportation planning. However, real data sharing is restricted by privacy, accessibility, and collection costs, making the generation of pseudo GPS trajectories that mimic real distributions a prominent research direction. Recently, diffusion models (e.g., DiffTraj) have achieved high fidelity in city-scale taxi trajectory generation.

Limitations of Prior Work: The authors identify three unavoidable gaps in SOTA methods. First, poor multi-scale capability: existing models are mostly effective at the city scale; metrics degrade sharply when expanding to metropolitan or national scales (Fig. 2a shows a cliff-like drop in DiffTraj precision as scale increases). Second, limited transport modes: most methods are trained only on taxi trajectories, failing to cover trains, cars, bicycles, and walking. Third, efficiency and robustness: diffusion frameworks rely on step-by-step denoising, requiring expensive multi-step iterations even with DDIM acceleration.

Key Challenge: The authors attribute the failure at multiple scales to two mechanism flaws in the diffusion paradigm. One is Signal-to-Noise Ratio (SNR) imbalance: as geographic range expands, fine-grained local trajectories occupy a negligible portion of the overall space, and the MSE objective magnifies scale imbalances. The other is fixed-magnitude noise addition: the forward process injects similar noise levels regardless of whether a trajectory is micro-short or macro-long, which is incompatible with data ranges spanning several orders of magnitude.

Goal / Key Insight: Instead of patching the diffusion framework, the authors switch to a new generative paradigm. Flow Matching directly regresses the target vector field along a predefined conditional probability path, bypassing the fixed-step denoising chain for more stable training and efficient sampling. This is combined with data-side "normalization-reconstruction" to explicitly compensate for scale imbalance.

Core Idea: Replace diffusion denoising with Flow Matching, overlaid with per-trajectory normalization, RDP compression, and OD condition prediction to address scalability, diversity, and efficiency in a unified framework.

Method¶

Overall Architecture¶

The input to TrajFlow is a set of "trajectory conditions" (departure time, regional OD, transport mode), and the output is a synthetic GPS trajectory. The pipeline consists of three stages: normalization and reconstruction (per-trajectory normalization to a bounded coordinate space + RDP geometric compression), transforming messy, multi-scale coordinates into a stable representation; Wide&Deep conditional encoding to fuse numerical and discrete features into a condition vector \(e_c\) for the backbone network; and Flow Matching training/inference in the normalized space—regressing the vector field on a linear path during training and performing ODE integration from Gaussian noise during inference.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Real GPS Trajectories<br/>(lat, lon, t) sequences"] --> B["Multi-scale Normalization & Reconstruction<br/>Per-trajectory Scaling + RDP Compression"]
    C["Trajectory Conditions<br/>Departure Time / OD / Mode"] --> D["Wide&Deep Encoding<br/>Numerical + Discrete → e_c"]
    B --> E["Flow Matching Training & Inference<br/>Linear Path Regression + OD Supervision"]
    D --> E
    E -->|~10 ODE steps| F["Denormalization + Resampling<br/>Mapping back to Geocoordinates"]
    F --> G["Synthetic Pseudo GPS Trajectories"]

Key Designs¶

1. Flow Matching over Diffusion: Avoiding Scale Mismatch with Deterministic Vector Fields

This paradigm innovation addresses the "fixed-magnitude noise" and "error accumulation" issues in diffusion. Flow Matching learns a time-dependent vector field \(v_\theta(x,t)\) to transport a simple prior \(p_0\) (Standard Gaussian) to the real distribution \(p_1\). Generation simply requires solving the ODE \(\frac{dx_t}{dt}=v_\theta(x_t,t)\). The authors use Conditional Flow Matching (CFM) with linear paths, where the target vector field is \(u_t(x\mid x_1)=x_1-x_0\):

\[\mathcal{L}_{FM}=\mathbb{E}_{t,\,p(x_1),\,p(x_0)}\Big[\big\|v_\theta\big((1-t)x_0+tx_1,\,t\big)-(x_1-x_0)\big\|^2\Big]\]

where \(t\sim\mathcal{U}[0,1]\). Compared to diffusion's multi-step denoising, CFM regresses the vector field directly per sample, leading to more stable training and 10-step inference. Flow Matching is more robust across heterogeneous regions because it avoids the fundamental mismatch caused by diffusion's scale-agnostic noise.

2. Multi-scale Trajectory Normalization & Reconstruction: Compressing Coordinates into Stable Representations

To address SNR imbalance, trajectories are independently normalized to a shared bounded coordinate space. The model predicts fine-grained points within this normalized space, which are then mapped back. This prevents micro-scale movements from being overwhelmed by large-scale changes and stabilizes gradients.

Geometric compression is applied via the Ramer–Douglas–Peucker (RDP) algorithm, which recursively removes redundant points within an \(\epsilon\) tolerance while preserving turns and high-curvature areas. This reduces trajectory length from \(L\) to \(D\) (\(D \ll L\)), lowering computational overhead and improving training stability.

3. Wide&Deep Conditioning + Fine OD Prediction: Context Injection and Endpoint Anchoring

Conditions are encoded using a Wide&Deep module: numerical features \(Z_n\) (speed, distance, etc.) produce \(e_{wide}\) via linear projection; discrete features \(Z_d\) (time, mode, regional OD) produce \(e_{deep}\) via embeddings and MLPs. They are fused as:

\[e_c=\text{LayerNorm}(e_{wide}+e_{deep})\]

The vector field is controlled by \(\tilde{e}=e_c+e_t\), injected via a learnable additive bias: \(h^{(\ell)}\leftarrow f^{(\ell)}(h^{(\ell)}+A^{(\ell)}\tilde{e})\). An auxiliary supervision loss for precise OD positions is introduced to enhance spatial and semantic awareness, contributing significantly to shape fidelity at large scales.

Loss & Training¶

The total loss comprises a masked regression loss on valid tokens (Flow Matching objective) and an auxiliary loss for fine-grained OD positions. During inference, the learned ODE is numerically integrated over \([0,1]\) starting from Gaussian noise \(x_0\), followed by resampling and denormalization to generate final trajectories.

Key Experimental Results¶

Main Results¶

Testing on the 2023 Blogwatcher dataset (millions of trajectories in Japan). Baselines include DiffTraj (Diffusion), TrajVAE (VAE), and TrajGAN (GAN). Evaluation includes spatial density (JS divergence) and trajectory similarity (DTW, Fréchet distance).

Scale	Method	Density JS ↓	DTW_med ↓	Fr_med ↓
Central Tokyo (City)	TrajFlow	0.0674	20.350	0.304
Central Tokyo	TrajFlow-w/o RDP&OD	0.0323	8.179	0.184
Central Tokyo	DiffTraj	0.1340	44.321	0.651
Tokyo Metro	TrajFlow	0.1239	18.167	0.335
Tokyo Metro	TrajFlow-w/o RDP&OD	0.0800	14.416	0.303
Tokyo Metro	DiffTraj	0.2918	88.559	1.220
Entire Japan (National)	TrajFlow	0.2270	10.977	0.192
Entire Japan	DiffTraj	0.6727	451.042	5.329
Entire Japan	TrajVAE	0.5228	135.377	2.216

Observations: At the city scale, the Flow Matching backbone (w/o RDP&OD) is sufficient. As the scale grows, the full TrajFlow (with OD/RDP) becomes dominant, while diffusion and other baselines degrade significantly.

Ablation Study¶

Configuration	Change	Description
Full TrajFlow	—	Most stable at national scale
w/o-FM	Replaced with DDPM denoising	Performance consistently inferior to FM, confirming FM as the primary driver
w/o-RDP	Removed RDP compression	Increases in Fr/DTW medians and tails; worse density JS at national scale
w/o-OD	Removed OD prediction	Consistent degradation in DTW/Fr; worse shape fidelity at national scale
w/o-RDP&OD	Removed both	Most severe degradation, highlighting importance at national scale

Key Findings¶

Flow Matching is the primary performance driver: CFM outperforms DDPM even with high step budgets, proving the paradigm shift is key to multi-scale fidelity.
Efficiency advantage: TrajFlow requires only ~10 ODE steps; DDPM fails to match TrajFlow's accuracy even at 300 steps.
Scale robustness: Diffusion's SNR issues aggregate in mixed-scale national data, whereas Flow Matching handles heterogeneous regions effectively.
Mode diversity: TrajFlow successfully matches the distribution of travel distances across four transportation modes.

Highlights & Insights¶

Paradigm shift over patching: Addressing diffusion's multi-scale failure by switching to Flow Matching simplifies the framework and removes long-chain error accumulation.
Complementary data and model strategies: RDP/Normalization fixes SNR imbalance while Flow Matching ensures efficient probabilistic transport.
Scale-adaptive component usage: The observation that certain components (RDP/OD) are essential only at larger scales suggests that normalization/reconstruction needs to be "scale-configured" in spatiotemporal tasks.

Limitations & Future Work¶

Lack of individual preferences: The model does not use user attributes (age, gender, home-work IDs) due to privacy, generating only group-level consistent trajectories.
Private/Single-country dataset: Generalization across different countries or data sources remains unverified.
Future directions: Extending TrajFlow to generalized human mobility modeling and developing adaptive methods for hyperparameters like RDP tolerance \(\epsilon\) and ODE steps.

vs. DiffTraj: DiffTraj suffers at metropolitan/national scales due to SNR and scale mismatch; TrajFlow reduces DTW/Fr/density JS by an order of magnitude with fewer steps.
vs. TrajVAE/TrajGAN: These methods struggle with stability and yield larger median errors on large-scale heterogeneous trajectories.
vs. Diffusion Acceleration: Unlike DDIM, which still requires iterative denoising, TrajFlow regresses the vector field directly, benefiting both efficiency and stability.

Rating¶

Novelty: ⭐⭐⭐⭐⭐ First use of Flow Matching for GPS trajectory generation; first to achieve nationwide multi-scale generation.
Experimental Thoroughness: ⭐⭐⭐⭐ Covers three scales, four baselines, and complete ablation; however, limited to a single private dataset.
Writing Quality: ⭐⭐⭐⭐ Clear logic from motivation to mechanism.
Value: ⭐⭐⭐⭐⭐ High utility for privacy-preserving nationwide movement modeling in urban planning and disaster response.