Zero-shot Geometry-Aware Diffusion Guidance for Music Restoration

Diffusion models have emerged as powerful generative frameworks and are increasingly used as foundational models for music generation tasks. Recent works have proposed various inference-time optimization methods to adapt pretrained models to downstream tasks. However, these approaches often push noisy samples away from the expected distribution in the diffusion reverse process when applying task-specific loss gradients. To address this issue, we propose Diffusion Geodesic Guidance (DGG), a geometry-aware method that operates on a pretrained diffusion prior preserving the distribution-induced geometry of noisy samples via a closed-form spherical linear interpolation. It updates noisy samples along geodesics of the underlying geometry. We then apply the zero-shot plug-and-play DGG to four multi-task music restoration tasks, achieving consistent improvements over existing training-free baselines and demonstrating a surprisingly wide range of applications for multi-task music restoration.