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Trajectory forecasting is critical for autonomous platforms to make safe planning and actions. Currently, most trajectory forecasting methods assume that object trajectories have been extracted and directly develop trajectory predictors based on the ground truth trajectories. However, this assumption does not hold in practical situations. Trajectories obtained from object detection and tracking are inevitably noisy, which could cause serious forecasting errors to predictors built on ground truth trajectories. In this paper, we propose a trajectory predictor directly based on detection results without relying on explicitly formed trajectories. Different from the traditional methods which encode the motion cue of an agent based on its clearly defined trajectory, we extract the motion information only based on the affinity cues among detection results, in which an affinity-aware state update mechanism is designed to take the uncertainty of association into account. In addition, considering that there could be multiple plausible matching candidates, we aggregate the states of them. This design relaxes the undesirable effect of noisy trajectory obtained from data association. Extensive ablation experiments validate the effectiveness of our method and its generalization ability on different detectors. Cross-comparison to other forecasting schemes further proves the superiority of our method. Code will be released upon acceptance.