# Idempotence and Perceptual Image Compression

arXiv: https://arxiv.org/abs/2401.08920 · HTML: https://mlsanity.com/paper/2401.08920/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 64 references that are in the map.
- First posted on arXiv 17 Jan 2024.

## Builds on (most cited first, 30 of 48)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Video Enhancement with Task-Oriented Flow](https://mlsanity.com/paper/1711.09078/) (2017)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Pivotal Tuning for Latent-based Editing of Real Images](https://mlsanity.com/paper/2106.05744/) (2021)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding](https://mlsanity.com/paper/2203.10886/) (2022)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [Channel-wise Autoregressive Entropy Models for Learned Image Compression](https://mlsanity.com/paper/2007.08739/) (2020)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Learned Image Compression with Mixed Transformer-CNN Architectures](https://mlsanity.com/paper/2303.14978/) (2023)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [Real-Time Adaptive Image Compression](https://mlsanity.com/paper/1705.05823/) (2017)
- [You Only Need Adversarial Supervision for Semantic Image Synthesis](https://mlsanity.com/paper/2012.04781/) (2020)
- [Improving Statistical Fidelity for Neural Image Compression with Implicit Local Likelihood Models](https://mlsanity.com/paper/2301.11189/) (2023)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)

## Built on by (most cited first, 29 of 29)

- [StableCodec: Taming One-Step Diffusion for Extreme Image Compression](https://mlsanity.com/paper/2506.21977/) (2025)
- [Compressed Image Generation with Denoising Diffusion Codebook Models](https://mlsanity.com/paper/2502.01189/) (2025)
- [OSCAR: One-Step Diffusion Codec Across Multiple Bit-rates](https://mlsanity.com/paper/2505.16091/) (2025)
- [Lossy Compression with Pretrained Diffusion Models](https://mlsanity.com/paper/2501.09815/) (2025)
- [DLF: Extreme Image Compression with Dual-generative Latent Fusion](https://mlsanity.com/paper/2503.01428/) (2025)
- [Lossless data compression by large models](https://mlsanity.com/paper/2407.07723/) (2024)
- [Ultra Lowrate Image Compression with Semantic Residual Coding and Compression-aware Diffusion](https://mlsanity.com/paper/2505.08281/) (2025)
- [Bidirectional Consistency Models](https://mlsanity.com/paper/2403.18035/) (2024)
- [PICD: Versatile Perceptual Image Compression with Diffusion Rendering](https://mlsanity.com/paper/2505.05853/) (2025)
- [CoD: A Diffusion Foundation Model for Image Compression](https://mlsanity.com/paper/2511.18706/) (2025)
- [PSC: Posterior Sampling-Based Compression](https://mlsanity.com/paper/2407.09896/) (2024)
- [Turbo-DDCM: Fast and Flexible Zero-Shot Diffusion-Based Image Compression](https://mlsanity.com/paper/2511.06424/) (2025)
- [Idempotent Unsupervised Representation Learning for Skeleton-Based Action Recognition](https://mlsanity.com/paper/2410.20349/) (2024)
- [Ultra-Low Bitrate Perceptual Image Compression with Shallow Encoder](https://mlsanity.com/paper/2512.12229/) (2025)
- [CoD-Lite: Real-Time Diffusion-Based Generative Image Compression](https://mlsanity.com/paper/2604.12525/) (2026)
- [Synonymous Variational Inference for Perceptual Image Compression](https://mlsanity.com/paper/2505.22438/) (2025)
- [Diff-ICMH: Harmonizing Machine and Human Vision in Image Compression with Generative Prior](https://mlsanity.com/paper/2511.22549/) (2025)
- [Next-Frame Decoding for Ultra-Low-Bitrate Image Compression with Video Diffusion Priors](https://mlsanity.com/paper/2603.15129/) (2026)
- [Survey on Visual Signal Coding and Processing with Generative Models: Technologies, Standards and Optimization](https://mlsanity.com/paper/2405.14221/) (2024)
- [SS-DC: Spatial-Spectral Decoupling and Coupling Across Visible-Infrared Gap for Domain Adaptive Object Detection](https://mlsanity.com/paper/2507.12017/) (2025)
- [Generative AI Meets 6G and Beyond: Diffusion Models for Semantic Communications](https://mlsanity.com/paper/2511.08416/) (2025)
- [TextBoost: Boosting Scene Text Fidelity in Ultra-low Bitrate Image Compression](https://mlsanity.com/paper/2603.04115/) (2026)
- [Towards Defining an Efficient and Expandable File Format for AI-Generated Contents](https://mlsanity.com/paper/2410.09834/) (2024)
- [Fast Training-free Perceptual Image Compression](https://mlsanity.com/paper/2506.16102/) (2025)
- [Keep It Real: Challenges in Attacking Compression-Based Adversarial Purification](https://mlsanity.com/paper/2508.05489/) (2025)
- [Dual-Constrained Diffusion Image Compression for Operational Rate-Distortion-Perception Optimization](https://mlsanity.com/paper/2606.13366/) (2026)
- [Group-of-Latents: Perceptual Video Compression at Extreme Bitrates via Masked Latent Generative Modeling](https://mlsanity.com/paper/2607.19437/) (2026)
- [H-DDCM: Hadamard Codebooks for Fast Generative Image and Video Compression](https://mlsanity.com/paper/2610.18125/) (2026)
- [Recasting DiT for Extreme Image Compression with Hierarchical Visual Priors](https://mlsanity.com/paper/2610.18607/) (2026)

## Abstract (arXiv)

Idempotence is the stability of image codec to re-compression. At the first glance, it is unrelated to perceptual image compression. However, we find that theoretically: 1) Conditional generative model-based perceptual codec satisfies idempotence; 2) Unconditional generative model with idempotence constraint is equivalent to conditional generative codec. Based on this newfound equivalence, we propose a new paradigm of perceptual image codec by inverting unconditional generative model with idempotence constraints. Our codec is theoretically equivalent to conditional generative codec, and it does not require training new models. Instead, it only requires a pre-trained mean-square-error codec and unconditional generative model. Empirically, we show that our proposed approach outperforms state-of-the-art methods such as HiFiC and ILLM, in terms of Fr'echet Inception Distance (FID). The source code is provided in https://github.com/tongdaxu/Idempotence-and-Perceptual-Image-Compression.