Learned image compression (LIC) has achieved remarkable coding efficiency, where entropy modeling plays a pivotal role in minimizing bitrate through informative priors. Existing methods predominantly exploit internal contexts within the input image, yet the rich external priors embedded in large-scale training data remain largely underutilized. Recent advances in dictionary-based entropy models have demonstrated that incorporating external priors can substantially enhance compression performance. However, current approaches organize heterogeneous external priors within a single-level dictionary, resulting in imbalanced utilization and limited representational capacity. Moreover, effective entropy modeling requires not only expressive priors but also a parameter estimation network capable of interpreting them. To address these challenges, we propose HiDE, a Hierarchical Dictionary-based Entropy modeling framework for learned image compression. HiDE decomposes external priors into global structural and local detail dictionaries with cascaded retrieval, enabling structured and efficient utilization of external information. Moreover, a context-aware parameter estimator with parallel multi-receptive-field design is introduced to adaptively exploit heterogeneous contexts for accurate conditional probability estimation. Experimental results show that HiDE achieves 18.5%, 21.99%, and 24.01% BD-rate savings over VTM-12.1 on the Kodak, CLIC, and Tecnick datasets, respectively.
Figures & tables
Figure 1: BD-Rate vs. decoding latency on the Kodak dataset (top-left indicates better performance).
Figure 2: Visualization of dictionary entry utilization. The top two rows show attention heatmaps from DCAE on Kodak images, highlighting the dominant entries in the retrieval process. The bottom row presents the mean attention scores of dictionary entries across the Kodak dataset, where DCAE’s single-level dictionary (left) exhibits a highly skewed usage, while our proposed Global (middle) and Detail (right) dictionaries achieve more balanced utilization.
Figure 3: Overview of the proposed HiDE framework. HiDE integrates hierarchical dictionaries ( δG,δD ) to retrieve external priors, which are fused with the hyperprior Fz and channel-wise autoregressive context. The aggregated context guides the entropy parameter estimator fE and the latent residual predictor fLRP to refine reconstruction quality and improve entropy modeling accuracy.
Figure 4: Overview of the proposed Hierarchical Dictionary-based Entropy Model, which consists of Hierarchical Dictionary-based Context Model (HD) and Context-aware Parameter Estimation (CaPE). Top-left: slice-wise entropy model that aggregates hyperprior Fz and autoregressive context yˉ<i . Top-right (blue box ei ): internal structure of the i -th slice network employing the Hierarchical Dictionary Cross-Attention (HDCA) module to retrieve external priors for parameter estimation ( fE ) and residual prediction ( fLRP ). Bottom (yellow box): HDCA performs a two-stage retrieval: first querying the Global Dictionary δG for global structural priors CGi , and then querying the Detail Dictionary δD for local detailed texture priors CDi conditioned on the global context. Bottom-right (pink box): fusion stages generating intermediate Xei and final dictionary-aware context Fdicti .
Figure 5: Illustration of the proposed Context-aware Parameter Estimation (CaPE) module. Left: CaPE was employed in two module in entropy model. Firstly, CaPE served as the parameter estimator fE extracts a shared context representation to predict both μ and σ . Then fLRP predicts the quantization residual r . Middle: The internal structure of the context extractor. Right: The task-specific heads for mean, scale, and residual prediction, implemented with lightweight stacked 3×3 convolutions and GELU activations.
Figure 6: Rate-distortion curve on three benchmark datasets: Kodak, Tecnick, and CLIC Professional Validation (From left to right).
Model
BD-Rate (%) w.r.t. VTM-12.0
Latency (ms)
Params (M)
GFLOPs
Kodak
Tecnick
CLIC
Total
Enc.
Dec.
PSNR
MS-SSIM
PSNR
PSNR
TCM (CVPR’23)
-11.97
–
-11.95
-11.96
220
120
100
75.9
700.65
MLIC+ (ACMMM’23)
-13.19
–
-17.47
-16.45
–
–
–
–
–
MLIC++ (ICMLW’23)
-15.09
–
-18.68
-16.84
235.4
106.5
128.9
116.7
615.93
FTIC (ICLR’24)
-14.84
-54.30
-15.24
-13.58
6846.6
1727.7
3391.9
69.78
245.46
Table 1: Comparison with state-of-the-art compression methods. BD-Rate is reported with respect to VTM-12.0. Latency, parameter count, and GFLOPs are measured on the Kodak dataset using one NVIDIA RTX 4090 GPU.
Model
BD-Rate (%)
Params (M)
+HD
-1.35
139.4
+CaPE
-2.82
114.4
HD + CaPE (HiDE)
-3.81
134.9
Table 2: Ablation of hierarchical dictionary (HD) and context-aware parameter estimation (CaPE) on the Kodak dataset. DCAE ( Lu et al., 2025 ) is used as the baseline.
Figure 7: Visualization of latent representations and predicted distribution parameters. From top to bottom: baseline DCAE, CaPE-only variant, and full HiDE (HD+CaPE). From left to right: latent slice, predicted mean, absolute prediction error (y−μ) , predicted scale σ , normalized residual (y−μ)/σ , and latent entropy map.
G - D
BD-Rate (%)
BD-PSNR (dB)
32–96
-1.26
0.060
64–64
-1.35
0.065
Table 3: Impact of different global–detail ( G–D ) dictionary size configurations under a fixed total dictionary capacity. DCAE ( Lu et al., 2025 ) serves as the baseline.
Model
BD-Rate (%)
Params (M)
Latency (ms)
TCM
-5.3
45.2
93
TCM + CaPE
-5.6
55.0
94
Table 4: Generalization of the context-aware parameter estimation (CaPE) module when applied to the small version of TCM ( Liu et al., 2023 ) framework. Results are reported with ( Cheng et al., 2020 ) as the anchor.
Entropy coding is widely used in typical learned image compression (LIC) that converts latents into a compact bitstream. However, entropy coding is typically sequential and becomes the coding latency bottleneck. To overcome it, we present Entropy-Coding Free Learned Image Compression (EF-LIC), a multi-rate framework that generates compact representation by removing statistical and correlation redundancy with low coding latency. First, we introduce unconstrained vector quantization and prove that its index distribution approaches the maximum-entropy bound, yielding minimal statistical redundancy. Second, we propose a context-conditioned autoregressive transform that directly reparameterizes the latents to reduce inter-dependency. Theoretical analysis shows that EF-LIC can remove correlation redundancy as effectively as typical LIC with entropy coding, leading to comparable compression performance. Experiments show EF-LIC achieves up to 67.86% bitrate reduction over MS-ILLM on Kodak with LPIPS. Ablation studies further show EF-LIC matches the compression performance of its entropy-coding based variant while achieving over 3× faster encoding and 5× faster decoding.
Hao Cao, Wenqi Guo, Zhijin Qin +1
Department of Electronic Engineering, Tsinghua University · Department of Automation, Tsinghua University · State Key Laboratory of Space Network and Communications +1
Most learned image compression systems rely on a single latent representation combined with a hyperprior, which limits their ability to efficiently capture image structure across spatial scales. In this work, we propose a hierarchical latent representation to improve the efficiency of the entropy model. By using multiple latents at different scales, each with its own entropy model, we better capture the spatial structure of the latent representation. Our experiments show that this approach achieves a 17.9% BD-rate reduction over VVC on Kodak, demonstrating the effectiveness of multi-scale latent representations. Furthermore, the approach is orthogonal to other advances in learned image compression, making it a versatile addition to existing methods.
Jonas Brenig, Radu Timofte
Computer Vision Lab, CAIDAS & IFI, University of Würzburg, Germany
Learned image compression has seen significant progress in recent years with the development of end-to-end learned models that achieve better compression efficiency than state-of-the-art conventional methods. Recently, Mixture of Experts (MoE) approaches have seen promising results in NLP and computer vision tasks. In this paper, we introduce the MoE approach to learned image compression. We propose a MoE-based Entropy model (MoEE) for learned image compression, allowing the model to selectively activate only the subset of parameters required for the input image. Our model achieves a BD-Rate improvement over VVC of -16.85% on the Kodak dataset.
Jonas Brenig, Radu Timofte
Computer Vision Lab, CAIDAS & IFI, University of Würzburg, Germany