Face restoration under complex degradations still remains an ill-posed inverse problem due to severe information loss. Although diffusion models benefit from strong generative priors, most methods still condition only on low-quality inputs, making it difficult to recover identity-critical details under heavy degradations. In this work, we propose HDRFace, a High-Dimensional Representation conditioned Face restoration framework that injects semantically rich priors into the conditional flow without modifying the generative backbone. Our pipeline first obtains a structurally reliable intermediate restoration with an off-the-shelf restorer, then uses a pretrained high-dimensional feature encoder to extract fine-grained facial representations from both the low-quality input and the intermediate result, and injects them as additional conditions for generation. We further introduce SDFM, a Structure-Detail aware adaptive Fusion Mechanism that emphasizes global constraints during structure modeling and strengthens representation guidance during detail synthesis, balancing structural consistency and detail fidelity. To validate the generalization ability of our method, we implement the proposed framework on two generative models, SD V2.1-base and Qwen-Image, and consistently observe stable and coherent performance gains across different architectures.