WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression

Yue Yu; Bowei Kang; Changsheng Gao; Dong Liu; Xiaoyan Sun

cs.CVOct 15, 2026

WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression

Authors: Yue Yu, Bowei Kang, Changsheng Gao, Dong Liu, Xiaoyan Sun

Organizations: University of Science and Technology of China, Hefei, China · MOE Key Laboratory of Brain-Inspired Intelligent Perception and Cognition, University of Science and Technology of China, Hefei, China · Nanyang Technological University, Singapore, Singapore · National Engineering Laboratory for Brain-inspired Intelligence Technology and Application; MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition, University of Science and Technology of China, Hefei, China ·

Abstract

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.

Figures & tables

Figure 1. Three paradigms for LLM-based lossless image compression and their performance. Left: pixel-domain methods ( Chen et al., 2025 ) linearize the image into a pixel sequence, residual-domain methods ( Du et al., 2025 ) code residuals from a lossy reconstruction, and WaveLLM decomposes the image into multiresolution wavelet subbands and models their coefficients. Right: lossless coding rates (bpsp, lower is better) on three benchmarks. A teaser figure contrasting three LLM-based compression paradigms and a grouped bar chart comparing coding rates across methods and benchmarks.

Figure 2. WaveLLM framework. Left: WaveLLM converts the input image to YCoCg, performs wavelet decomposition, and entropy-codes the resulting subbands using arithmetic coding. Within this coding pipeline, the learnable entropy-modeling core consists of task prompt construction, the coding-oriented numerical interface, and a shared LoRA-adapted LLM that outputs coefficient probability distributions. Decoding follows the symmetric path for exact reconstruction. Right: expanded task prompt for a representative $HL_{l}$ task, including the natural-language text prompt and the serialized value sequence formed by same-level $LL_{l}$ context and $HL_{l}$ target values. A framework diagram of WaveLLM. Left: the WaveLLM coding pipeline with color transform, wavelet decomposition, remapping, arithmetic coding, and exact reconstruction together with the entropy-modeling core. Right: an expanded task prompt for a representative HL subband, showing the text prompt and the serialized value sequence derived from same-level LL context and HL target values.

Figure 3. Within-level coding order and same-level context at level

l

. The red arrows indicate

LL_{l}\rightarrow HL_{l}\rightarrow LH_{l}\rightarrow HH_{l}

; correspondingly,

HL_{l}

uses

LL_{l}

LH_{l}

uses

[LL_{l},HL_{l}]

, and

HH_{l}

uses

[LL_{l},HL_{l},LH_{l}]

. A two-panel diagram showing, at one wavelet level, the spatial arrangement of LL, HL, LH, and HH with red arrows indicating the coding order on the left, and the equivalent same-level dependency graph for the three high-frequency subbands on the right.

Figure 4. LLM entropy model. Text prompts use the frozen text embedding module, while coefficients are remapped to local IDs and embedded by a dedicated value embedding module. The assembled task sequence is processed by the LoRA-adapted backbone, and a value prediction head outputs probabilities over the local value range for arithmetic coding. Architecture diagram showing two input paths (value sequence and text prompt), task-specific sequence assembly, a LoRA-adapted pretrained LLM, and a value prediction head producing a probability distribution.

Item	Setting
Backbone	Llama-3.2-3B (frozen)
Adaptation	LoRA (shared across all tasks)
LoRA rank / alpha / dropout	128 / 256 / 0.05
Target modules	q/k/v/o + gate/up/down proj.
Color transform	reversible YCoCg
Wavelet transform	4-level fixed 5/3 lifting

Table 1. Implementation settings.

Category	Codec	Kodak	CLIC.pro	DIV2K
Traditional	PNG	4.35 +73.3%	3.93 +75.4%	4.23 +86.3%
	JPEG2000	3.19 +27.1%	2.93 +30.8%	3.12 +37.4%
	JPEG-LS	3.16 +25.9%	2.82 +25.9%	2.99 +31.7%
	FLIF	2.90 +15.5%	2.72 +21.4%	2.91 +28.2%
	JPEG XL	2.87 +14.3%	2.63 +17.4%	2.79 +22.9%
Learned	L3C ( Mentzer et al., 2019 )	3.26 +29.9%	2.94 +31.2%	3.09 +36.1%

Table 2. Lossless coding performance (bpsp) under reported settings; green percentages show bitrate increase over WaveLLM. Training data and auxiliary signals differ across papers.

Method	kMACs/px	Enc. (s)	Dec. (s)	Hardware
iWave (PixelCNN)	—	582.9	611.6	RTX 3090
Delétang et al. (8B)	$2.1\!\times\!10^{7}$	10.44	288.0	4 $\times$ A100
P 2 -LLM (8B)	—	14.9	273.1	8 $\times$ A800
Visual Prompt (8B)	$4.2\!\times\!10^{7}$	21.1	495.6	4 $\times$ A100
WaveLLM (3B)	$2.6\!\times\!10^{7}$	65.1	152.8	8 $\times$ RTX 3090

Table 3. Per-image runtime on Kodak (

768\times 512

), including arithmetic coding and I/O. iWave and WaveLLM are measured in our environment; other entries are quoted from prior work on different hardware. The kMACs/pixel column reports multiply-accumulate operations per output pixel where available.

Domain	Side information	Kodak	CLIC.pro	DIV2K
Pixel	none	2.72 +8.4%	2.35 +4.9%	2.44 +7.5%
Residual	lossy thumb.	2.97 +18.3%	2.43 +8.5%	2.48 +9.3%
Wavelet	same-level context	2.51	2.24	2.27

Table 4. Coding-domain comparison under the same 3B setup. Pixel uses rasterized RGB; Residual codes residuals using the global lossy image and corresponding local reconstruction patch as prompts; Wavelet codes integer subband coefficients with same-level context. Green percentages indicate relative bitrate increase over Wavelet. Lower is better.

Entropy model / Backbone	Kodak	CLIC.pro	DIV2K
PixelCNN (iWave)	2.94 +17.1%	2.60 +16.1%	2.73 +20.3%
WaveLLM-1B	2.88 +14.7%	2.41 +7.6%	2.50 +10.1%
WaveLLM-3B	2.51	2.24	2.27

Table 5. Lossless coding performance (bpsp) within the same reversible wavelet codec. The transform, coding order, and arithmetic coder are fixed; only the entropy model changes. Green percentages indicate the relative bitrate increase over WaveLLM-3B. Lower is better.

Figure 5. Wavelet-domain local gain and rate contribution on Kodak01. Rows follow LL/HL/LH/HH and columns follow Levels 4 to 1. Left: $\Delta$ Subband BPSP $=$ BPSP ${}_{\text{iWave}}$ $-$ BPSP ${}_{\text{WaveLLM}}$ ; right: each subband’s absolute contribution to the final WaveLLM bitrate. Warmer colors indicate larger values. Two side-by-side 4 by 4 wavelet-structured heatmaps for Kodak01, showing local coding gain on the left and each subband's absolute contribution to the final WaveLLM bitrate on the right.

Figure 6. Actual coefficient and LLM-predicted peak-value distributions for four Kodak01 subbands. Each pair compares the two distributions at matched positions.

LL_{4}

is shown in coefficient space after converting MED residuals back; the remaining pairs show

HL_{3}

LH_{3}

, and

HH_{3}

. A violin plot comparing actual coefficient-value distributions and LLM-predicted peak-value distributions for Kodak01 on four subbands: LL4 on the left, followed by HL3, LH3, and HH3. Each subband has two violins labeled Actual and Predicted.

	Prompt	Val. IF	HF scope	MED	Kodak ( $\Delta$ )	CLIC.pro ( $\Delta$ )
(a) Full system	$\checkmark$	ded.	same	$\checkmark$	2.51	2.24
(b) $-$ prompt	$\times$	ded.	same	$\checkmark$	2.62 ( $+$ 0.11)	2.45 ( $+$ 0.21)
(c) $-$ val. IF	$\checkmark$	res.	same	$\checkmark$	2.58 ( $+$ 0.07)	2.32 ( $+$ 0.08)
(d) $-$ HF ctx	$\checkmark$	ded.	LL	$\checkmark$	2.54 ( $+$ 0.03)	2.30 ( $+$ 0.06)
(e) $+$ parent HF	$\checkmark$	ded.	same+par.	$\checkmark$	2.74 ( $+$ 0.23)	2.51 ( $+$ 0.27)
(f) $-$ MED	$\checkmark$	ded.	same	$\times$	2.52 ( $+$ 0.01)	2.27 ( $+$ 0.03)

Table 6. Ablations of WaveLLM (bpsp). Each row changes one design choice relative to the full system (a).

\Delta

: rate increase (positive = worse). Val. IF: value interface. HF scope: same = same-level, LL = LL-only, +par. = same + parent-level.

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Learned Image Compression Lossless Data Compression

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Large language model (LLM)-based lossless image compression methods typically represent pixel data through the native text interface of a pretrained model, converting pixel values into token sequences that the LLM processes through its vocabulary head. This design shows that pretrained language models can provide probability estimates for image coding, but it also couples compression to tokenizer behavior, vocabulary-specific numeric tokens, and model-family-specific adaptation. In this paper, we present LUMI (LLM-based Unified Model-agnostic lossless Image compression), a tokenizer-agnostic framework for lossless RGB image compression with frozen LLM backbones. LUMI replaces pixel-as-text tokenization with a pixel embedding module that maps raw intensity and channel information into the continuous embedding space of the LLM. It further introduces intra-patch position encoding to retain two-dimensional spatial structure after flattening, and uses a 256-way prediction head to produce probabilities over the native pixel alphabet. Only the pixel embedding, position encoding, soft-prefix parameters, and prediction head are trained, while the LLM backbone remains fixed. Experiments on natural, medical, and remote-sensing image benchmarks with LLaMA, Qwen, and Gemma backbones show that LUMI provides a unified interface across tokenizer families, achieves competitive compression rates, and improves cross-domain robustness over tokenizer-based LLM compression baselines. These results formulate LLM-based lossless image compression as pixel-space adaptation of frozen foundation models rather than tokenizer-specific language-symbol modeling.

Abstract

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