Lossless image compression fundamentally relies on accurate entropy modeling, driving a recent shift toward large language model (LLM)-based methods. However, existing approaches mainly emphasize the modeling capacity of LLMs while directly serializing images into pixel or residual sequences, leaving heterogeneous signal patterns entangled within a single prediction stream. In this paper, we argue that effective entropy modeling depends not only on model capacity, but also on the predictability of the input representation. Motivated by this insight, we propose WaveLLM, a wavelet-domain LLM-based entropy model for lossless image compression. By decomposing an image into multi-level wavelet subbands, WaveLLM converts a heterogeneous prediction problem into a set of more structured and statistically homogeneous subproblems that are more amenable to autoregressive probability estimation. To bridge numerical coding symbols with the LLM's native text token space, we introduce a dedicated numerical interface featuring value embeddings and a coefficient prediction head. Furthermore, a task-adaptive prompting strategy is designed to enable a single shared model to adapt to diverse subbands within a unified framework. Built on Llama-3.2-3B with LoRA adaptation, WaveLLM achieves 2.51, 2.24, and 2.27 bpsp on Kodak, CLIC.pro, and DIV2K, respectively, outperforming the PixelCNN-based codec using the same wavelet transform by 0.43, 0.36, and 0.46 bpsp, and surpassing recent LLM-based lossless compressors on all three benchmarks.

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