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Medical image restoration is essential for improving the usability of noisy, incomplete, and artifact-corrupted clinical scans, yet existing methods often rely on task-specific retraining and offer limited control over the trade-off between faithful reconstruction and prior-driven enhancement. This lack of controllability is especially problematic in clinical settings, where overly aggressive restoration may introduce hallucinated details or alter diagnostically important structures. In this work, we propose CARE, a training-free controllable restoration framework for real-world medical images that explicitly balances structure preservation and prior-guided refinement during inference. CARE uses a dual-latent restoration strategy, in which one branch enforces data fidelity and anatomical consistency while the other leverages a generative prior to recover missing or degraded information. A risk-aware adaptive controller dynamically adjusts the contribution of each branch based on restoration uncertainty and local structural reliability, enabling conservative or enhancement-focused restoration modes without additional model training. We evaluate CARE on noisy and incomplete medical imaging scenarios and show that it achieves strong restoration quality while better preserving clinically relevant structures and reducing the risk of implausible reconstructions and show that it achieves strong restoration quality while better preserving clinically relevant structures and reducing the risk of implausible reconstructions. The proposed approach offers a practical step toward safer, more controllable, and more deployment-ready medical image restoration.