Deep unfolding networks (DUNs) combine the interpretability of model-based methods with the learning ability of deep networks, yet remain limited for blind image restoration (BIR). Existing DUNs suffer from: (1) \textbf{Degradation-specific dependency}, as their optimization frameworks are tied to a known degradation model, making them unsuitable for BIR tasks; and (2) \textbf{Over-smoothing bias}, resulting from the direct feeding of gradient descent outputs, dominated by low-frequency content, into the proximal term, suppressing fine textures. To overcome these issues, we propose UnfoldLDM to integrate DUNs with latent diffusion model (LDM) for BIR. In each stage, UnfoldLDM employs a multi-granularity degradation-aware (MGDA) module as the gradient descent step. MGDA models BIR as an unknown degradation estimation problem and estimates both the holistic degradation matrix and its decomposed forms, enabling robust degradation removal. For the proximal step, we design a degradation-resistant LDM (DR-LDM) to extract compact degradation-invariant priors from the MGDA output. Guided by this prior, an over-smoothing correction transformer (OCFormer) explicitly recovers high-frequency components and enhances texture details. This unique combination ensures the final result is degradation-free and visually rich. Experiments show that our UnfoldLDM achieves a leading place on various BIR tasks and benefits downstream tasks. Moreover, our design is compatible with existing DUN-based methods, serving as a plug-and-play framework. Code will be released.