Bound-Conditioned Latent Inference for Progressive Image Compression

Jaeseok Jang; Seungmin Jeon; Kwang Pyo Choi; Chang-Su Kim

eess.IVOct 22, 2026

Bound-Conditioned Latent Inference for Progressive Image Compression

Authors: Jaeseok Jang, Seungmin Jeon, Kwang Pyo Choi, Chang-Su Kim

Organizations: Korea University · Samsung Electronics

Abstract

Progressive image compression reconstructs images from prefixes of a single bitstream and therefore involves sequential latent inference under partial observations. Existing trit-plane codecs mainly treat decoded trits as discrete symbols for probability prediction, without fully exploiting their role as interval constraints on the underlying continuous latents. We propose bound-conditioned latent inference (BLI), a framework that reformulates progressive trit-plane coding as sequential latent inference under shrinking interval constraints. At each coding step, the trits decoded so far define lower and upper bounds for each latent element. BLI uses the center and width of these bounds, together with hyperprior information shared by the encoder and decoder, to jointly refine the Gaussian parameters $(μ,σ)$ for entropy modeling and the latent estimate $\hat{y}$ for reconstruction. As additional trits are decoded, the feasible intervals shrink monotonically, yielding tighter constraints for the next inference step and enabling flexible in-plane refinement schedules. Experiments on Kodak, CLIC, and JPEG-AI show that BLI achieves state-of-the-art rate-distortion performance among progressive image codecs, reducing BD-rate by $17.78\%$ over DPICT and by $7.96\%$ over CTC on Kodak, while replacing CTC's plane-specific predictors with a shared model that uses about $5.3\times$ fewer parameters and achieves lower latency than CTC.

Figures & tables

Figure 1: Rate-allocation maps of the proposed bound-conditioned latent inference (BLI) codec. Each column corresponds to the same trit-plane level, i.e. , the same degree of latent quantization, while each row uses a different number of in-plane refinement steps. The top row encodes an entire trit-plane in a single step, whereas the middle and bottom rows divide each trit-plane into two and four substeps, respectively. Colors indicate spatial rate allocation, with warmer colors corresponding to higher coding rates and cooler colors to lower rates. More frequent bound-conditioned updates iteratively refine the latent distribution within the same quantization level, yielding better rate efficiency without changing the final trit-plane precision.

Figure 2: Overview of the BLI process. At coding step $k$ , the trits decoded so far define bound tensors $(\mathbf{C}^{k-1},\mathbf{D}^{k-1})$ , which represent the current feasible ranges of latent elements. Given these bounds and the hyperprior parameters $(\mathbf{M}^{0},\mathbf{\Sigma}^{0})$ , BLI estimates the Gaussian parameters $(\mathbf{M}^{k},\mathbf{\Sigma}^{k})$ for entropy coding and the latent tensor $\hat{\mathbf{Y}}^{k-1}$ for reconstruction under the current bounds. After a subset of trits is decoded using $(\mathbf{M}^{k},\mathbf{\Sigma}^{k})$ , the bounds are updated to $(\mathbf{C}^{k},\mathbf{D}^{k})$ , yielding tighter feasible ranges that, in turn, are used in the next coding step. This step-wise process iteratively refines the latent distribution and reconstruction.

Figure 3: Illustration of the BLI refinement process using a 1D sequence of latent elements. Given the current bounds $(\mathbf{C}^{k-1},\mathbf{D}^{k-1})$ , BLI estimates $(\mathbf{M}^{k},\mathbf{\Sigma}^{k})$ for entropy coding and $\hat{\mathbf{Y}}^{k-1}$ for reconstruction under those bounds. After selected trits are decoded, the bounds are updated to $(\mathbf{C}^{k},\mathbf{D}^{k})$ , yielding tighter feasible intervals for the next BLI step. Red dots denote original latent values, blue dots denote latent estimates, and blue densities denote estimated Gaussian distributions.

Figure 4: Architecture of the BLI module. BLI predicts the Gaussian parameters $(\mathbf{M}^{k},\mathbf{\Sigma}^{k})$ and the latent estimate $\hat{\mathbf{Y}}^{k-1}$ from the current bounds and hyperprior parameters.

Figure 5: R-D curves on Kodak against traditional, fixed-rate learned, and progressive learned codecs. The left plot reports PSNR, and the right plot reports MS-SSIM in dB.

Table 6

Figure 6: Qualitative comparison against representative traditional and progressive codecs.

Figure 7: Qualitative comparison with existing trit-plane codecs at trit-plane endpoints. Within each column, the same number of trits is transmitted for all three codecs. The numbers below each result indicate bpp and PSNR.

Figure 8: Step-wise updates to predicted Gaussian distributions for two latent elements during evaluation. We compare BLI with method I, the ablation variant without the bound-width input and interval-rescaled output constraint. Colors transition from blue to red as decoding proceeds.

Table 11

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 10: R-D curve comparison of the proposed BLI codec with existing progressive and fixed-rate image codecs. From top to bottom, the rows correspond to Kodak, CLIC 2021, and JPEG-AI. Best viewed digitally with zooming.

		PSNR			MS-SSIM
		Kodak	CLIC	JPEG-AI	Kodak	CLIC	JPEG-AI
Traditional	JPEG2000 [ Skodras et al., 2001 ]	$47.54$	$58.41$	$55.73$	$183.09$	$232.17$	$205.86$
	BPG444 [ Bellard, 2014 ]	$-7.92$	$0.21$	$0.74$	$64.25$	$74.67$	$89.49$
	VTM 12.0 [ Bross et al., 2021 ]	$-2.14$	$-2.17$	$-0.85$	$69.49$	$72.06$	$94.68$
Fixed-rate	STF [ Zou et al., 2022 ]	$-14.85$	$-12.87$	$-11.69$	$-12.64$	$-7.73$	$-5.57$
	LIC-TCM [ Liu et al., 2023 ]	$-18.69$	$-19.37$	$-18.18$	$-13.84$	$-7.74$	$-6.53$

Appendix

Table 6: BD-rates (%) with respect to FTIC-DPICT.

\mathbf{C}^{0}_{i}\leftarrow\mathbf{M}^{0}_{i},\qquad\mathbf{D}^{0}_{i}\leftarrow 3^{n_{i}}.

Appendix

Algorithm 1 Encoding in BLI

\mathbf{C}^{0}_{i}\leftarrow\mathbf{M}^{0}_{i},\qquad\mathbf{D}^{0}_{i}\leftarrow 3^{n_{i}}.

Appendix

Algorithm 2 Decoding in BLI

Method	FLOPs (T)	Neural inference (s)	Non-neural processing (s)	Total latency (s)
FTIC-DPICT	41.42	0.08	5.77	5.85
FTIC-CTC	66.69	0.18	6.44	6.62
BLI	65.96	3.72	1.05	4.77

Appendix

Table 7: Comparison of computational complexity on the Kodak dataset.

Trans. ordering	Full BD-rate (%)	Endpoint BD-rate (%)
Random	$-10.01$	$-19.63$
Raster scan	$-7.62$	$-18.52$
$\sigma$ ascending	$-2.47$	$-18.02$
R-D prioritized	$\mathbf{-17.78}$	$-19.59$

Appendix

Table 8: Effect of the within-plane transmission ordering on the Kodak dataset. BD-rates (%) are measured relative to FTIC-DPICT.

Test-time variant	Entropy params. for coding	Latent recon.	BD-rate (%)
Recon. with Gaussian mean	$(\mathbf{M}^{k},\mathbf{\Sigma}^{k})$	Gaussian mean	$-16.38$
No entropy refinement	$(\mathbf{M}^{0},\mathbf{\Sigma}^{0})$	$\hat{\mathbf{Y}}^{k-1}$	$-10.24$
Full BLI	$(\mathbf{M}^{k},\mathbf{\Sigma}^{k})$	$\hat{\mathbf{Y}}^{k-1}$	$\mathbf{-17.78}$

Appendix

Table 9: Test-time ablation of entropy modeling and latent reconstruction on the Kodak dataset. BD-rates (%) are measured relative to FTIC-DPICT.

bpp	Metric	BPG444	VTM 12.0	FTIC-DPICT	FTIC-CTC	BLI
0.10	LPIPS	0.3848	0.3494	0.4008	0.3465	0.3203
	DISTS	0.2038	0.1994	0.2308	0.2089	0.1910
0.15	LPIPS	0.3207	0.3064	0.3569	0.3123	0.2868
	DISTS	0.1771	0.1800	0.2049	0.1884	0.1736
0.20	LPIPS	0.2760	0.2663	0.3045	0.2661	0.2366
	DISTS	0.1586	0.1606	0.1780	0.1630	0.1510

Appendix

Table 10: Comparison of perceptual quality on the Kodak dataset at low bitrates. Lower LPIPS and DISTS values indicate better perceptual quality.

Figure 11: Progressively reconstructed images of ‘kodim04.png’ and ‘kodim18.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 12: Progressively reconstructed images of ‘kodim08.png’ and ‘kodim13.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 13: Progressively reconstructed images of ‘kodim21.png’ and ‘kodim22.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 14: Progressively reconstructed images of ‘andrew-ruiz-376.png’ and ‘clem-onojeghuo-33741.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 15: Progressively reconstructed images of ‘daniel-robert-405.png’ and ‘mullermarc-184.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 16: Progressively reconstructed images of ‘thong-vo-428.png’ and ‘vita-vilcina-3055.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 17: Progressively reconstructed images of ‘00002_TE_2144x1424.png’ and ‘00003_TE_1944x1296.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 18: Progressively reconstructed images of ‘00005_TE_1336x872.png’ and ‘00009_TE_1976x1312.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 19: Progressively reconstructed images of ‘00010_TE_2000x1128.png’ and ‘00011_TE_1744x1160.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

Figure 20: Progressively reconstructed images of ‘img_1280x720_3x8bit_RGB_color_SMPTE_RP_219_2002.png’ and ‘img_1280x720_3x8bit_RGB_color_rainbow_gradient.png’ obtained by the PSNR-trained model. The bitrate (bpp), PSNR (dB), and MS-SSIM (dB) are reported below each image.

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Efficient Learned Image Compression without Entropy Coding

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Learned Image Compression Vector Quantization

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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\times

faster encoding and

5\times

faster decoding.

Abstract

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