# Diffusion^2: Dual Diffusion Model with Uncertainty-Aware Adaptive Noise for Momentary Trajectory Prediction

arXiv: https://arxiv.org/abs/2510.04365 · HTML: https://mlsanity.com/paper/2510.04365/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 44 of its 64 references that are in the map.
- First posted on arXiv 5 Oct 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, 30 of 44)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting](https://mlsanity.com/paper/2012.01526/) (2020)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [AR-Diffusion: Auto-Regressive Diffusion Model for Text Generation](https://mlsanity.com/paper/2305.09515/) (2023)
- [Peeking into the Future: Predicting Future Person Activities and Locations in Videos](https://mlsanity.com/paper/1902.03748/) (2019)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [SGCN:Sparse Graph Convolution Network for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2104.01528/) (2021)
- [SocialVAE: Human Trajectory Prediction using Timewise Latents](https://mlsanity.com/paper/2203.08207/) (2022)
- [Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs](https://mlsanity.com/paper/2305.03935/) (2023)
- [TRiPOD: Human Trajectory and Pose Dynamics Forecasting in the Wild](https://mlsanity.com/paper/2104.04029/) (2021)
- [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023)
- [Three Steps to Multimodal Trajectory Prediction: Modality Clustering, Classification and Synthesis](https://mlsanity.com/paper/2103.07854/) (2021)
- [Stochastic Image Denoising by Sampling from the Posterior Distribution](https://mlsanity.com/paper/2101.09552/) (2021)
- [EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2307.09306/) (2023)
- [How many Observations are Enough? Knowledge Distillation for Trajectory Forecasting](https://mlsanity.com/paper/2203.04781/) (2022)
- [SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model](https://mlsanity.com/paper/2403.18452/) (2024)

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

- [URAG: A Benchmark for Uncertainty Quantification in Retrieval-Augmented Large Language Models](https://mlsanity.com/paper/2603.19281/) (2026)

## Abstract (arXiv)

Accurate pedestrian trajectory prediction is crucial for ensuring safety and efficiency in autonomous driving and human-robot interaction scenarios. Earlier studies primarily utilized sufficient observational data to predict future trajectories. However, in real-world scenarios, such as pedestrians suddenly emerging from blind spots, sufficient observational data is often unavailable (i.e. momentary trajectory), making accurate prediction challenging and increasing the risk of traffic accidents. Therefore, advancing research on pedestrian trajectory prediction under extreme scenarios is critical for enhancing traffic safety. In this work, we propose a novel framework termed Diffusion^2, tailored for momentary trajectory prediction. Diffusion^2 consists of two sequentially connected diffusion models: one for backward prediction, which generates unobserved historical trajectories, and the other for forward prediction, which forecasts future trajectories. Given that the generated unobserved historical trajectories may introduce additional noise, we propose a dual-head parameterization mechanism to estimate their aleatoric uncertainty and design a temporally adaptive noise module that dynamically modulates the noise scale in the forward diffusion process. Empirically, Diffusion^2 sets a new state-of-the-art in momentary trajectory prediction on ETH/UCY and Stanford Drone datasets.