Multi-modal brain imaging with MRI, CT, and PET has significantly advanced our understanding of cognition and neurodisease by providing complementary information. However, constraints on scan time and cost often result in missing critical high-quality sequences. Existing cross-modality synthesis methods are typically task- or modality-specific, leading to performance degradation when applied to heterogeneous real-world imaging data. Here, we propose UniSyn, a unified framework capable of synthesizing target imaging modalities with specific acquisition parameters from any available ones, guided by metadata. UniSyn first learns robust metadata representations through image-text alignment on large-scale multimodal neuroimaging datasets. We then introduce a cross-modality synthesis framework that leverages learned metadata representations to guide the generation of metadata-specified target images. To enhance interpretable metadata-driven control over image synthesis across diverse protocols, we design a dual-parameter arithmetic operation that explicitly integrates source and target metadata into the image translation process. Extensive experiments on multi-institutional brain imaging datasets demonstrate that UniSyn surpasses the existing cross-modality synthesis approaches in both quantitative fidelity and clinical relevance, enabling the generation of missing imaging counterparts tailored to specific clinical and research needs.