Diffusion models have been achieving remarkable performance in face restoration. However, the heavy computations hamper the widespread adoption of these models. In this work, we propose QuantFace, a novel low-bit quantization framework for face restoration models, where the full-precision (i.e., 32-bit) weights and activations are quantized to 4~6-bit. We first analyze the data distribution within activations and find that it is highly variant. To preserve the original data information, we employ rotation-scaling channel balancing. Furthermore, we propose Quantization-Distillation Low-Rank Adaptation (QD-LoRA), which jointly optimizes for quantization and distillation performance. Finally, we propose an adaptive bit-width allocation strategy. We formulate such a strategy as an integer programming problem that combines quantization error and perceptual metrics to find a satisfactory resource allocation. Extensive experiments on the synthetic and real-world datasets demonstrate the effectiveness of QuantFace under 6-bit and 4-bit. QuantFace achieves significant advantages over recent leading low-bit quantization methods for face restoration. The code is available at https://github.com/jiatongli2024/QuantFace.