Value Prediction is a long-standing technique to boost instruction-level parallelism by speculatively breaking data dependencies through predicting register-write values. Existing state-of-the-art predictors, such as EVES, combine computational and context-based approaches but still rely exclusively on local value history, limiting their ability to capture broader correlations. Global value prediction, which exploits correlations across multiple dynamic instructions, has been explored only sparingly. The gDiff predictor first demonstrated the potential of global stride correlations, and EgDiff recently improved upon it with practical refinements. However, both remain PC-localized and thus fail to exploit per-path correlations, where global correlations vary across execution paths. In this work, we propose CgDiff, the first context-based global value predictor. CgDiff augments stride-based global prediction with control-flow history to capture path-sensitive global correlations that elude existing designs. Our evaluation shows that a compact 8.92KB CgDiff not only surpasses a much larger 44KB EgDiff, but also outperforms the state-of-the-art EVES predictor in IPC speedup. Furthermore, a storage-efficient 16.92KB hybrid (CgDiff + EVES) achieves the highest performance among all predictors under comparable budgets. These results demonstrate that context-based global value prediction is a powerful and storage-efficient complement to existing local designs, opening a promising new direction for future research in value prediction.