# Vehicle Trajectory Prediction Using Residual Diffusion Model Based on Image Information
## 1 Introduction  
In the field of vehicle trajectory prediction based on visual sensors, the core task is to predict the future trajectory of a moving vehicle using information such as historical trajectories, road maps and traffic lights as modeling conditions. Achieving safe navigation in complex environments is a key task in autonomous driving technology, which is directly related to the reliability and practicability of the autonomous driving system. To this end, autonomous vehicles usually need to rely on vision sensors to obtain detailed information about their surroundings and predict the future trajectories of other vehicles based on this information. Research on trajectory prediction is mainly divided into two categories: classical physical models and deep learning models. Traditional research is mainly based on Kalman filter [1], hidden Markov model [2] and other kinematic theories to describe and predict car motion. These algorithms do not need training samples, and have simple structures and high efficiency. However, since the driving intentions of nearby vehicles are often unknown, it becomes extremely challenging to accurately predict their future motion trajectories. In complex traffic scenarios, each vehicle forms its behavior through complex interactions with other vehicles, which often interferes with prediction methods that rely on physical constraints, making it more difficult to predict the joint trajectory of multiple vehicles in the scene simultaneously. Deep learning algorithms optimize model parameters by using massive data to achieve accurate simulation of a variety of future motion scenarios. Social LSTM [3] is the firstto propose a \"social pooling layer\" that allows neighboring vehicles to share moving trajectories as a way to deal with the inherent uncertainty of trajectories. Social GAN (SGAN) [4] employs a strategy based on generative adversarial networks for learning models and motion trajectories from global or neighboring vehicles. However, this approach presents challenges in terms of training stability and naturalness of trajectories. CVAE [5; 6] adopts the variational Autoencoder (VAE) framework to introduce hidden variables that have important effects on vehicle trajectory distribution into the model. CS-LSTM [7] uses a convolutional pooling module to encode adjacent vehicle trajectories, and applies a graph-theoretic approach to handle complex traffic scenarios. Autonomous driving is a multi-agent task. Therefore, applying reinforcement learning to develop explicit multi-agent methods to learn autonomous vehicles is an important future research direction [8; 9]. In recent years, denoising diffusion probabilistic models(DDPM) [10; 11] have emerged as an efficient method for image generation and a powerful tool for sound synthesis [12]. On this basis, some scholars have proposed a new method based on seq-to-seq [13] model. However, due to the tedious process of denoising and the need for a large number of operations, it is difficult to directly apply the traditional denoising methods to the field of trajectory prediction. In order to solve this problem, a new method is proposed: Denoising Diffusion implicit Model (DDIM) [14], which first predicts the original data, and then uses a non-Markovian method to predict the generation direction at the next time. On this basis, Probabilistic Diffusion (PD) [15] proposes the use of a deterministic diffusion sampler for knowledge distillation in the denoising process and an iterative approach to improve the efficiency of the sampling process. In the field of trajectory prediction, motion indeterminacy diffusion (MID) [16] is the first denoising diffusion model for trajectory prediction in the world, and fully considers the inherent uncertainty in trajectory generation. Because the generation process requires a large number of denoising steps to ensure the accuracy of the trajectory. In order to deal with this challenge, some scholars further proposed the Leapfrog diffusion model [17] (LED).