Understanding and Mitigating the High Computational Cost in Path Data Diffusion

TL;DR

This work tackles the high computational cost of graph-space diffusion for Path Generation (PG) by introducing Latent-space Path Diffusion (LPD), which transfers diffusion to a latent representation learned via an encoder–decoder. LPD uses a VAE-style Transformer encoder and a causal decoder to map paths to a compact latent space, where a DDPM-based diffusion model operates, enabling efficient unconditional and conditional path generation. Empirical results on two city road networks show substantial time and memory savings (up to ~82.8% and ~83.1%) while achieving state-of-the-art or competitive path-generation performance (24.5–34.0% improvement over GPD). This work highlights latent diffusion as a promising direction for scalable PG and offers a foundation for extending latent diffusion to broader spatiotemporal trajectory tasks, with future work aimed at generalization across road networks.

Abstract

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%.

Figures (12)

• Figure 1: A toy example for Transition Probability Matrix (TPM) in GPD method.
• Figure 2: Rank and singular values change.
• Figure 3: Time comparison between linear/exponential strategy.
• Figure 4: Time cost breakdown.
• Figure 5: Our encoder-decoder framework.