# Leveraging the Spatial Hierarchy: Coarse-to-fine Trajectory Generation via Cascaded Hybrid Diffusion

arXiv: https://arxiv.org/abs/2507.13366 · HTML: https://mlsanity.com/paper/2507.13366/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 76 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [InterDiff: Generating 3D Human-Object Interactions with Physics-Informed Diffusion](https://mlsanity.com/paper/2308.16905/) (2023)
- [Latent Diffusion for Language Generation](https://mlsanity.com/paper/2212.09462/) (2022)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Recurrent Neural Networks (RNNs): A gentle Introduction and Overview](https://mlsanity.com/paper/1912.05911/) (2019)
- [DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Model](https://mlsanity.com/paper/2304.11582/) (2023)
- [PLANNER: Generating Diversified Paragraph via Latent Language Diffusion Model](https://mlsanity.com/paper/2306.02531/) (2023)
- [LSTM-TrajGAN: A Deep Learning Approach to Trajectory Privacy Protection](https://mlsanity.com/paper/2006.10521/) (2020)
- [ControlTraj: Controllable Trajectory Generation with Topology-Constrained Diffusion Model](https://mlsanity.com/paper/2404.15380/) (2024)
- [ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2307.00754/) (2023)
- [Continuous Trajectory Generation Based on Two-Stage GAN](https://mlsanity.com/paper/2301.07103/) (2023)

## Built on by (most cited first, 4 of 4)

- [Towards Generalizable Human Activity Recognition: A Survey](https://mlsanity.com/paper/2508.12213/) (2025)
- [Learning Demographic-Conditioned Mobility Trajectories with Aggregate Supervision](https://mlsanity.com/paper/2603.03275/) (2026)
- [From GPS Points to Travel Patterns: Flexible and Semantic Trajectory Generation with LLMs](https://mlsanity.com/paper/2605.30014/) (2026)
- [Plan-to-Synthesis: Cross-City Human Mobility Generation via Semantic Latent Flow Matching](https://mlsanity.com/paper/2609.32732/) (2026)

## Abstract (arXiv)

Urban mobility data has significant connections with economic growth and plays an essential role in various smart-city applications. However, due to privacy concerns and substantial data collection costs, fine-grained human mobility trajectories are difficult to become publicly available on a large scale. A promising solution to address this issue is trajectory synthesizing. However, existing works often ignore the inherent structural complexity of trajectories, unable to handle complicated high-dimensional distributions and generate realistic fine-grained trajectories. In this paper, we propose Cardiff, a coarse-to-fine Cascaded hybrid diffusion-based trajectory synthesizing framework for fine-grained and privacy-preserving mobility generation. By leveraging the hierarchical nature of urban mobility, Cardiff decomposes the generation process into two distinct levels, i.e., discrete road segment-level and continuous fine-grained GPS-level: (i) In the segment-level, to reduce computational costs and redundancy in raw trajectories, we first encode the discrete road segments into low-dimensional latent embeddings and design a diffusion transformer-based latent denoising network for segment-level trajectory synthesis. (ii) Taking the first stage of generation as conditions, we then design a fine-grained GPS-level conditional denoising network with a noise augmentation mechanism to achieve robust and high-fidelity generation. Additionally, the Cardiff framework not only progressively generates high-fidelity trajectories through cascaded denoising but also flexibly enables a tunable balance between privacy preservation and utility. Experimental results on three large real-world trajectory datasets demonstrate that our method outperforms state-of-the-art baselines in various metrics.