Zero-shot image restoration provides a flexible way to handle diverse degradations without task-specific training. However, existing methods typically rely on stacked layers or pre-trained features to enhance degradation expression, while overlooking physically consistent priors. The insufficient degradation prompts impose the heavy training burden and high sampling costs during zero-shot diffusion. Moreover, the fixed inference trajectory often collapses to suboptimal solutions under complex corruptions. We observe that heterogeneous degradations can be reparameterized into a minimal set of physically coherent parameters for compact representation. Based on this insight, we first propose a unified physical zero-shot image restoration (UP-ZeroIR) framework that explicitly models heterogeneous degradations into a homogeneous all-in-one distribution. The distribution can be optimized directly in the latent space, enabling principled solution exploration and effective prompt adaptation. Besides, we introduce a dynamic quality-refinement strategy that adaptively adjusts the diffusion trajectory for robust globally optimal convergence. Extensive experiments demonstrate that our method achieves state-of-the-art performance across both single and mixed degradations. Our code is available at https://github.com/yangjinglyy/UP-ZeroIR