This paper presents a framework for single-frame face super-resolution that is robust to variations in head pose, facial expression, and illumination. The framework uses a redundant transformation with diagonal loading to model mappings between different facial factors, and local reconstruction with geometry and position constraints to incorporate image details into new factor spaces. Experimental results demonstrate that the proposed framework offers robustness when dealing with inputs with different expressions, poses, and illuminations compared to other methods, can generate higher resolution faces with better quality than tensor-based methods, and improves on previous work by producing multiple outputs with varied factors rather than a single output.