By optimizing the rate-distortion-realism trade-off, generative image compression approaches produce detailed, realistic images instead of the only sharp-looking reconstructions produced by rate-distortion-optimized models. In this paper, we propose a novel deep learning-based generative image compression method injected with diffusion knowledge, obtaining the capacity to recover more realistic textures in practical scenarios. Efforts are made from three perspectives to navigate the rate-distortion-realism trade-off in the generative image compression task. First, recognizing the strong connection between image texture and frequency-domain characteristics, we design a Fractal Frequency-Aware Band Image Compression (FFAB-IC) network to effectively capture the directional frequency components inherent in natural images. This network integrates commonly used fractal band feature operations within a neural non-linear mapping design, enhancing its ability to retain essential given information and filter out unnecessary details. Then, to improve the visual quality of image reconstruction under limited bandwidth, we integrate diffusion knowledge into the encoder and implement diffusion iterations into the decoder process, thus effectively recovering lost texture details. Finally, to fully leverage the spatial and frequency intensity information, we incorporate frequency- and content-aware regularization terms to regularize the training of the generative image compression network. Extensive experiments in quantitative and qualitative evaluations demonstrate the superiority of the proposed method, advancing the boundaries of achievable distortion-realism pairs, i.e., our method achieves better distortions at high realism and better realism at low distortion than ever before.