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Spike-based imaging, inspired by the human visual system, offers several advantages, including high temporal resolution and low power consumption, but suffers from significant image degradation in low-light conditions due to noise interference. Restoring spike images under such conditions poses a significant challenge, as traditional frame-based or spike-based techniques are ill-suited to handle such severe noise and unique noise characteristics. This paper proposes a novel approach for restoring low-light spike images using noise-modeled diffusion models. By establishing a noise-embedded spike imaging model under low light, we model the forward diffusion process as the degradation of spike images with proportional and residual terms and incorporate deterministic and non-deterministic components with reverse shifting, enabling the model to capture the distinctive spike noise structure. Additionally, we utilize region mask image, dark current map and spike density value as conditions to further guide the restoration process by providing prompts for degradation regions, deterministic parameters and noise intensity, respectively. Experimental results demonstrate that our method significantly outperforms existing spike-based reconstruction and diffusion-based image restoration methods in both quantitative performance and visual quality. The code and dataset are available at https://github.com/BIT-Vision/SpikeDiffusion.