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Diffusion models have achieved remarkable progress in universal image restoration. However, existing methods perform naive inference in the reverse process, which leads to cumulative errors under limited sampling steps and large step intervals. Moreover, they struggle to balance the commonality of degradation representations with restoration quality, often depending on complex compensation mechanisms that enhance fidelity at the expense of efficiency. To address these challenges, we introduce \textbf{DGSolver}, a diffusion generalist solver with universal posterior sampling. We first derive the exact ordinary differential equations for generalist diffusion models to unify degradation representations and design tailored high-order solvers with a queue-based accelerated sampling strategy to improve both accuracy and efficiency. We then integrate universal posterior sampling to better approximate manifold-constrained gradients, yielding a more accurate noise estimation and correcting errors in inverse inference. Extensive experiments demonstrate that DGSolver outperforms state-of-the-art methods in restoration accuracy, stability, and scalability, both qualitatively and quantitatively. Code and models are publicly available at https://github.com/MiliLab/DGSolver.