Occlusion, a pervasive challenge in Multi-Object Tracking (MOT) within complex scenes, severely degrades tracking performance. Current methods still face numerous problems when handling occlusions. Motion prediction struggles to accommodate diverse motion patterns, resulting in failure during short-term occlusions. Concurrently, appearance features possess insufficient discriminative power under occluded conditions, which frequently leads to identity switches following long-term occlusion. To enhance the performance of MOT under such challenging conditions, we propose an innovative Occlusion-Aware Multi-Object Tracking via Joint Diffusion Motion Prediction and Appearance Purification (OAMOT). For short-term occlusions, a Diffusion Motion Recovery Model (DMRM) is developed, which integrates residual and noise diffusion branches to recover trajectories precisely under varied motion patterns. For long-term occlusions, the SAM Appearance Purification for ReID (SAPR) module is proposed; the module leverages the mask generation mechanism of SAM as foreground attention to enhance feature discriminability. Furthermore, a Lightweight Attention Predictor (LAP) is integrated into the ReID network to achieve SAM-quality attention during inference without significant computational overhead. Experimental results on the MOT17, MOT20, and DanceTrack datasets demonstrate that the proposed OAMOT method outperforms current state-of-the-art multi-object tracking techniques across multiple evaluation metrics. The code can be available on https://github.com/wangtuo111/OAMOT.