Marine towed-streamer seismic surveys inherently lack near-offset data due to physical constraints in source-receiver separation. This missing data significantly degrades critical processing workflows including multiple elimination, velocity analysis, and full-waveform inversion, ultimately impacting subsurface imaging quality. Therefore, we develop a self-supervised deep learning framework based on diffusion models that successfully reconstructs these missing near-offset traces without requiring unavailable ground-truth near-offset data for training. The method learns complex wave propagation patterns from the recorded far-offset data and progressively extrapolates toward zero offset. Validation experiments demonstrate substantial improvements over conventional methods, while real-world deployment on two field datasets confirms practical viability.