Rethinking Diffusion Model in High Dimension

Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that they can learn the statistical properties of the underlying probability distribution, enabling sampling from this distribution to generate realistic samples. But is this really how they work? To address this question, this paper conducts a detailed analysis of the objective function and inference methods of diffusion models, leading to several important conclusions that help answer the above question: 1) In high-dimensional sparse scenarios, the target of the objective function fitting degrades from a weighted sum of multiple samples to a single sample. 2) The mainstream inference methods can all be represented within a simple unified framework, without requiring statistical concepts such as Markov chains and SDEs. 3) Guided by this simple framework, more efficient inference methods can be discovered.

Network-Wide Traffic Flow Estimation Across Multiple Cities with Global Open Multi-Source Data: A Large-Scale Case Study in Europe and North America

Network-wide traffic flow, which captures dynamic traffic volume on each link of a general network, is fundamental to smart mobility applications. However, the observed traffic flow from sensors is usually limited across the entire network due to the associated high installation and maintenance costs. To address this issue, existing research uses various supplementary data sources to compensate for insufficient sensor coverage and estimate the unobserved traffic flow. Although these studies have shown promising results, the inconsistent availability and quality of supplementary data across cities make their methods typically face a trade-off challenge between accuracy and generality. In this research, we first time advocate using the Global Open Multi-Source (GOMS) data within an advanced deep learning framework to break the trade-off. The GOMS data primarily encompass geographical and demographic information, including road topology, building footprints, and population density, which can be consistently collected across cities. More importantly, these GOMS data are either causes or consequences of transportation activities, thereby creating opportunities for accurate network-wide flow estimation. Furthermore, we use map images to represent GOMS data, instead of traditional tabular formats, to capture richer and more comprehensive geographical and demographic information. To address multi-source data fusion, we develop an attention-based graph neural network that effectively extracts and synthesizes information from GOMS maps while simultaneously capturing spatiotemporal traffic dynamics from observed traffic data. A large-scale case study across 15 cities in Europe and North America was conducted. The results demonstrate stable and satisfactory estimation accuracy across these cities, which suggests that the trade-off challenge can be successfully addressed using our approach.