Generative models are prone to hallucinations: plausible but incorrect structures absent in the ground truth. This issue is problematic in image restoration for safety-critical domains such as medical imaging, industrial inspection, and remote sensing, where such errors undermine reliability and trust. For example, in low-field MRI, widely used in resource-limited settings, restoration models are essential for enhancing low-quality scans, yet hallucinations can lead to serious diagnostic errors. Progress has been hindered by a circular dependency: evaluating hallucinations requires labeled data, yet such labels are costly and subjective. We introduce HalluGen, a diffusion-based framework that synthesizes realistic hallucinations with controllable type, location, and severity, producing perceptually realistic but semantically incorrect outputs (segmentation IoU drops from 0.86 to 0.36). Using HalluGen, we construct the first large-scale hallucination dataset comprising 4,350 annotated images derived from 1,450 brain MR images for low-field enhancement, enabling systematic evaluation of hallucination detection and mitigation. We demonstrate its utility in two applications: (1) benchmarking image quality metrics and developing Semantic Hallucination Assessment via Feature Evaluation (SHAFE), a feature-based metric with soft-attention pooling that improves hallucination sensitivity over traditional metrics; and (2) training reference-free hallucination detectors that generalize to real restoration failures. Together, HalluGen and its open dataset establish the first scalable foundation for evaluating hallucinations in safety-critical image restoration.