# Understanding and Mitigating the High Computational Cost in Path Data Diffusion

arXiv: https://arxiv.org/abs/2502.00725 · HTML: https://mlsanity.com/paper/2502.00725/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 2 Feb 2025.

## Builds on (most cited first, 9 of 9)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)

## Built on by (most cited first, 1 of 1)

- [Uncertainty-Aware Generative Oversampling Using an Entropy-Guided Conditional Variational Autoencoder](https://mlsanity.com/paper/2509.25334/) (2025)

## Abstract (arXiv)

Advancements in mobility services, navigation systems, and smart transportation technologies have made it possible to collect large amounts of path data. Modeling the distribution of this path data, known as the Path Generation (PG) problem, is crucial for understanding urban mobility patterns and developing intelligent transportation systems. Recent studies have explored using diffusion models to address the PG problem due to their ability to capture multimodal distributions and support conditional generation. A recent work devises a diffusion process explicitly in graph space and achieves state-of-the-art performance. However, this method suffers a high computation cost in terms of both time and memory, which prohibits its application. In this paper, we analyze this method both theoretically and experimentally and find that the main culprit of its high computation cost is its explicit design of the diffusion process in graph space. To improve efficiency, we devise a Latent-space Path Diffusion (LPD) model, which operates in latent space instead of graph space. Our LPD significantly reduces both time and memory costs by up to 82.8% and 83.1%, respectively. Despite these reductions, our approach does not suffer from performance degradation. It outperforms the state-of-the-art method in most scenarios by 24.5%~34.0%.