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PMA-Diffusion: A Physics-guided Mask-Aware Diffusion Framework for TSE from Sparse Observations

Lindong Liu, Zhixiong Jin, Seongjin Choi

TL;DR

PMA-Diffusion tackles high-resolution traffic state estimation from sparse sensor data by learning a mask-aware diffusion prior directly from incomplete observations and applying a physics-guided posterior sampler. The approach decouples prior learning from inference, using an ambient-diffusion training with Single-mask and Double-mask strategies and a physics projector based on adaptive anisotropic smoothing to enforce traffic-wave structure during sampling. Experiments on I-24 MOTION demonstrate that the Double-mask training nearly reaches the fully supervised upper bound and substantially outperforms baselines under severe sparsity, showing strong robustness to sensor layouts. The framework provides a flexible, uncertainty-aware solution for TSE under realistic sensing sparsity and masking patterns with potential for extension to richer physics constraints and modalities.

Abstract

High-resolution highway traffic state information is essential for Intelligent Transportation Systems, but typical traffic data acquired from loop detectors and probe vehicles are often too sparse and noisy to capture the detailed dynamics of traffic flow. We propose PMA-Diffusion, a physics-guided mask-aware diffusion framework that reconstructs unobserved highway speed fields from sparse, incomplete observations. Our approach trains a diffusion prior directly on sparsely observed speed fields using two mask-aware training strategies: Single-Mask and Double-Mask. At the inference phase, the physics-guided posterior sampler alternates reverse-diffusion updates, observation projection, and physics-guided projection based on adaptive anisotropic smoothing to reconstruct the missing speed fields. The proposed framework is tested on the I-24 MOTION dataset with varying visibility ratios. Even under severe sparsity, with only 5% visibility, PMA-Diffusion outperforms other baselines across three reconstruction error metrics. Furthermore, PMA-diffusion trained with sparse observation nearly matches the performance of the baseline model trained on fully observed speed fields. The results indicate that combining mask-aware diffusion priors with a physics-guided posterior sampler provides a reliable and flexible solution for traffic state estimation under realistic sensing sparsity.

PMA-Diffusion: A Physics-guided Mask-Aware Diffusion Framework for TSE from Sparse Observations

TL;DR

PMA-Diffusion tackles high-resolution traffic state estimation from sparse sensor data by learning a mask-aware diffusion prior directly from incomplete observations and applying a physics-guided posterior sampler. The approach decouples prior learning from inference, using an ambient-diffusion training with Single-mask and Double-mask strategies and a physics projector based on adaptive anisotropic smoothing to enforce traffic-wave structure during sampling. Experiments on I-24 MOTION demonstrate that the Double-mask training nearly reaches the fully supervised upper bound and substantially outperforms baselines under severe sparsity, showing strong robustness to sensor layouts. The framework provides a flexible, uncertainty-aware solution for TSE under realistic sensing sparsity and masking patterns with potential for extension to richer physics constraints and modalities.

Abstract

High-resolution highway traffic state information is essential for Intelligent Transportation Systems, but typical traffic data acquired from loop detectors and probe vehicles are often too sparse and noisy to capture the detailed dynamics of traffic flow. We propose PMA-Diffusion, a physics-guided mask-aware diffusion framework that reconstructs unobserved highway speed fields from sparse, incomplete observations. Our approach trains a diffusion prior directly on sparsely observed speed fields using two mask-aware training strategies: Single-Mask and Double-Mask. At the inference phase, the physics-guided posterior sampler alternates reverse-diffusion updates, observation projection, and physics-guided projection based on adaptive anisotropic smoothing to reconstruct the missing speed fields. The proposed framework is tested on the I-24 MOTION dataset with varying visibility ratios. Even under severe sparsity, with only 5% visibility, PMA-Diffusion outperforms other baselines across three reconstruction error metrics. Furthermore, PMA-diffusion trained with sparse observation nearly matches the performance of the baseline model trained on fully observed speed fields. The results indicate that combining mask-aware diffusion priors with a physics-guided posterior sampler provides a reliable and flexible solution for traffic state estimation under realistic sensing sparsity.

Paper Structure

This paper contains 32 sections, 23 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Model-Driven and Data-Driven Approaches for TSE
  4. Physics-Informed Deep Learning (PIDL) for TSE
  5. Traffic State Estimation as an Inverse Problem
  6. Inverse problems and the position of TSE
  7. Diffusion models as generative priors for inverse problems and TSE
  8. Methodology
  9. Problem Setting
  10. Observation measurement
  11. Empirical evidence and assumptions
  12. Bayesian posterior perspective
  13. Mask-Aware Diffusion Prior
  14. Mask-selection strategies
  15. Mask-aware training process
  16. ...and 17 more sections

Figures (8)

  • Figure 1: Overall pipeline of the proposed PMA-Diffusion framework.
  • Figure 2: Matrix representation of traffic state variables collected from probe vehicles and loop detectors.
  • Figure 3: Illustration of two mask strategy. Left: original observed data under the single-mask strategy, reflecting actual sparse sensor coverage. Right: the same frame with further masked pixels, simulating the observation pattern under the double-mask strategy.
  • Figure 4: Random speed field samples from I-24 MOTION dataset. These samples illustrate the spatial-temporal structure (propagating waves, lane heterogeneity) that the model is required to learn.
  • Figure 5: Observation Patterns from Loop detectors and Probe vehicles. Dark areas denote unobserved pixels; colored entries denote observed speeds.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2