# ProDiff: Prototype-Guided Diffusion for Minimal Information Trajectory Imputation

arXiv: https://arxiv.org/abs/2505.23048 · HTML: https://mlsanity.com/paper/2505.23048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 24 of its 59 references that are in the map.
- First posted on arXiv 29 May 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Spatio-Temporal Self-Supervised Learning for Traffic Flow Prediction](https://mlsanity.com/paper/2212.04475/) (2022)
- [Deep Gravity: enhancing mobility flows generation with deep neural networks and geographic information](https://mlsanity.com/paper/2012.00489/) (2020)
- [ControlTraj: Controllable Trajectory Generation with Topology-Constrained Diffusion Model](https://mlsanity.com/paper/2404.15380/) (2024)
- [Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction](https://mlsanity.com/paper/2303.16005/) (2023)
- [Continuous Trajectory Generation Based on Two-Stage GAN](https://mlsanity.com/paper/2301.07103/) (2023)
- [AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction](https://mlsanity.com/paper/2402.03784/) (2024)
- [CDSA: Cross-Dimensional Self-Attention for Multivariate, Geo-tagged Time Series Imputation](https://mlsanity.com/paper/1905.09904/) (2019)
- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [RNTrajRec: Road Network Enhanced Trajectory Recovery with Spatial-Temporal Transformer](https://mlsanity.com/paper/2211.13234/) (2022)
- [Future Directions in Human Mobility Science](https://mlsanity.com/paper/2408.00702/) (2024)
- [AttnMove: History Enhanced Trajectory Recovery via Attentional Network](https://mlsanity.com/paper/2101.00646/) (2021)
- [Micro-Macro Spatial-Temporal Graph-based Encoder-Decoder for Map-Constrained Trajectory Recovery](https://mlsanity.com/paper/2404.19141/) (2024)
- [Full Bayesian Significance Testing for Neural Networks](https://mlsanity.com/paper/2401.13335/) (2024)

## Abstract (arXiv)

Trajectory data is crucial for various applications but often suffers from incompleteness due to device limitations and diverse collection scenarios. Existing imputation methods rely on sparse trajectory or travel information, such as velocity, to infer missing points. However, these approaches assume that sparse trajectories retain essential behavioral patterns, which place significant demands on data acquisition and overlook the potential of large-scale human trajectory embeddings. To address this, we propose ProDiff, a trajectory imputation framework that uses only two endpoints as minimal information. It integrates prototype learning to embed human movement patterns and a denoising diffusion probabilistic model for robust spatiotemporal reconstruction. Joint training with a tailored loss function ensures effective imputation. ProDiff outperforms state-of-the-art methods, improving accuracy by 6.28% on FourSquare and 2.52% on WuXi. Further analysis shows a 0.927 correlation between generated and real trajectories, demonstrating the effectiveness of our approach.