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.

翻译：幂等性是图像编解码器对重压缩的稳定性。初看之下，它与感知图像压缩并无关联。然而，我们理论发现：1）基于条件生成模型的感知编解码器满足幂等性；2）带幂等性约束的无条件生成模型等价于条件生成编解码器。基于这一新发现的等价关系，我们提出了一种通过施加幂等性约束来反转无条件生成模型的感知图像编解码新范式。我们的编解码器理论上等价于条件生成编解码器，且无需训练新模型，仅需预训练的均方误差编解码器和无条件生成模型。实验表明，我们提出的方法在弗雷歇初始距离（FID）指标上优于HiFiC和ILLM等最先进方法。源代码见https://github.com/tongdaxu/Idempotence-and-Perceptual-Image-Compression。