用频域建模提升图像压缩效率，保持重建确定性。

Generative models have significantly improved the performance ceiling of image lossy compression at low bitrates by exploiting learned priors. However, the generated textures and semantic details may deviate from the source content, thereby affecting the fidelity of image reconstruction. To solve these challenges, we propose FLM, a frequency-aware language model that improves compression efficiency through frequency-domain probabilistic modeling while retaining deterministic reconstruction. At the encoder, the input image is transformed into quantized DCT coefficients, which are organized into discrete sequences using macroblock-based coefficient tokenization. FLM then performs next-coefficient prediction to autoregressively estimate token-wise conditional probability distributions for arithmetic coding, thereby generating a compact bitstream. At the decoder, the LLM and arithmetic decoder jointly recover the frequency-domain data, followed by inverse transformations for image reconstruction. A task-specific frequency-domain dataset and a two-stage fine-tuning strategy are further developed to enable the model to operate across multiple bitrate settings. FLM is a versatile compressor that is compatible with both lossy compression and lossless JPEG recompression frameworks. Experiments show that FLM exceeds conventional and generative lossy compression methods in rate-distortion performance. FLM achieves BD-PSNR gains of 3.30 dB, 3.83 dB, and 3.80 dB than JPEG baseline on Kodak, Tecnick, and CLIC2020, respectively. Better qualitative quality of FLM can be achieved in improving semantically high fidelity and suppressing blocking artifacts. FLM is also validated to be applicable to the lossless recompression task with competitive performance.