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Idempotence and Perceptual Image Compression
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Shows theoretically that conditional generative perceptual codecs are idempotent and that inverting an unconditional diffusion model under an idempotence constraint is equivalent to them, yielding a training-free perceptual codec built on a pre-trained MSE codec.
Problem
Perceptual image compression typically needs a new conditional generative decoder per codec and bitrate, and the link between codec idempotence (stability under re-compression) and perceptual quality is unexplored.
Approach
Proves that a deterministic-encoder conditional generative codec is idempotent, and that sampling an unconditional generative model subject to f(X)=Y yields the same posterior; uses DPS-style diffusion inversion with a pre-trained MSE codec's encoder as the consistency term to decode perceptual reconstructions without training new models.</12core_idea>
Key results
- Proposed (ELIC) achieves the lowest BD-FID on all four datasets, e.g. -54.89 on FFHQ vs -50.58 for ILLM and -48.35 for HiFiC.
- Proposed approach keeps MSE within twice the base MSE codec bound (e.g. MSE 161.9 vs bound 183.5 for ELIC on FFHQ at 0.07 bpp).
- Using the proposed inversion as an idempotence improvement reduces re-compression MSE, e.g. ELIC from 11.80 to 7.367.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use unconditional DDPM inversion with the ELIC base codec | Proposed perceptual codec · FFHQ | BD-FID: -52.32 -> -54.89 | Helped |
| use unconditional DDPM inversion with the ELIC base codec | Proposed perceptual codec · ImageNet | BD-FID: -48.84 -> -55.18 | Helped |
| use unconditional DDPM inversion with the ELIC base codec | Proposed perceptual codec · COCO | BD-FID: -50.81 -> -58.45 | Helped |
| use unconditional DDPM inversion with the ELIC base codec | Proposed perceptual codec · CLIC | BD-FID: -42.96 -> -46.52 | Helped |
| use DDPM + DPS inversion instead of StyleGAN2 + PULSE, StyleGAN2 + ILO, or DDPM + MCG (ablation) | Proposed codec with ELIC on FFHQ · FFHQ | FID: 15.33 -> 5.347; 26.15 -> 5.347; 135.1 -> 5.347 | Helped |
| use DDPM + DPS inversion instead of StyleGAN2 + PULSE, StyleGAN2 + ILO, or DDPM + MCG (ablation) | Proposed codec with ELIC on FFHQ · FFHQ | MSE: 754.2 -> 161.9; 689.2 -> 161.9; 929.2 -> 161.9 | Helped |
| use x-domain instead of y-domain idempotence constraint (ablation) | DDPM + DPS with ELIC · FFHQ | FID: 5.377 -> 5.347 | No clear effect |
| use x-domain instead of y-domain idempotence constraint (ablation) | DDPM + DPS with ELIC · FFHQ | MSE: 189.2 -> 161.9 | Helped |
| add the proposed perceptual reconstruction step before re-compression | Hyper codec · Re-compression | MSE: 6.321 -> 2.850 | Helped |
| add the proposed perceptual reconstruction step before re-compression | ELIC codec · Re-compression | MSE: 11.80 -> 7.367 | Helped |
| increase DPS constraint strength ζ from too small to a suitable value (ablation) | DDPM + DPS codec · ImageNet with ELIC | reconstruction MSE | Helped |
| increase DPS constraint strength ζ too far (ablation) | DDPM + DPS codec · ImageNet with ELIC | reconstruction MSE | Hurt |
Surprising findings
- Proposed approach does not outperform LPIPS-trained codecs in LPIPS and MS-SSIM, where the MSE codec ELIC scores higher than the perceptual codecs.
- StyleGAN2-based inversion (PULSE, ILO) and MCG yield MSE far above the 2x MSE bound, so only DPS with DDPM passes the bound in the ablation.
Limitations
- Testing time is about 60 s per image due to gradient-based inversion versus about 0.1 s for HiFiC/ILLM.
- Fixed 256x256 resolution because unconditional generative models are not resolution-flexible; patch-based workaround causes consistency issues.
- Requires per-image tuning of the zeta step size and an adaptive multiplier to satisfy the MSE bound.
Experimental setup
Datasets: FFHQ ImageNet COCO CLIC 2020
Benchmarks: FFHQ ImageNet COCO CLIC 2020
Metrics: FID BD-FID BD-PSNR MSE PSNR KID LPIPS MS-SSIM
Baselines: HiFiC ILLM Po-ELIC CDC BPG VTM Hyper ELIC
Builds on: DPS MCG PULSE ILO HiFiC
Closest papers by meaning
- Idempotent Generative Network (ICLR 2024 · similarity 0.83)
- Good, Cheap, and Fast: Overfitted Image Compression with Wasserstein Distortion (CVPR 2025 · similarity 0.83)
- One-Step Diffusion-Based Image Compression with Semantic Distillation (NeurIPS 2025 · similarity 0.83)
- Towards image compression with perfect realism at ultra-low bitrates (ICLR 2024 · similarity 0.83)
- Decouple Distortion from Perception: Region Adaptive Diffusion for Extreme-low Bitrate Perception Image Compression (CVPR 2025 · similarity 0.83)
- Synonymous Variational Inference for Perceptual Image Compression (ICML 2025 · similarity 0.83)
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