Multi-Object Tracking (MOT) is a task in computer vision that involves simultaneously detecting, localizing, and maintaining identity consistency of multiple objects across consecutive video frames. However, in complex real-world scenarios, targets often exhibit nonlinear and diverse motion characteristics, such as sudden velocity changes and irregular trajectories. These characteristics pose significant challenges to traditional tracking methods that rely on linear motion models like the Kalman Filter. To tackle this issue, we propose GDMETracker, a novel real-time MOT framework. At the core of GDMETracker is the Grouped Diffusion-Based Motion Estimator (GDME), a hybrid motion prediction module that combines a neural network for feature learning with a generative diffusion probabilistic model. This module improves nonlinear motion prediction by incorporating a grouped modulation layer into the neural network, enabling fine-grained processing of complex motion patterns. By leveraging a learnable denoising diffusion process, GDME can learn the prior distribution of complex motion patterns from historical data, enabling it to generate precise predictions of future states based on past trajectories. GDMETracker demonstrates strong performance on the challenging DanceTrack [28] and SportsMOT [7] benchmarks, achieving HOTA scores of 62.5% and 72.6%, respectively, validating its effectiveness in handling dynamic and unpredictable motion scenarios.