The paper explores the relationship between idempotence and perceptual image compression, two seemingly unrelated concepts in image coding. Idempotence refers to the stability of image compression when re-compressed, while perceptual image compression aims to preserve visual quality. The authors find that: 1. **Conditional Generative Model and Idempotence**: A conditional generative model-based image codec is idempotent, meaning that re-compressing the reconstructed image results in the same output. 2. **Unconditional Generative Model and Perceptual Quality**: An unconditional generative model with an idempotence constraint is equivalent to a conditional generative model-based image codec, achieving perceptual quality. Based on these findings, the authors propose a new paradigm for perceptual image compression by inverting an unconditional generative model with idempotence constraints. This approach does not require training new models and is theoretically equivalent to conditional generative codecs. Empirical results show that this method outperforms state-of-the-art perceptual image codecs in terms of Fréchet Inception Distance (FID) while maintaining low complexity during testing. The paper also discusses the practical implementation details, including the use of pre-trained models and different constraints for idempotence. It compares the proposed method with existing techniques and highlights its advantages in terms of perceptual quality and efficiency.The paper explores the relationship between idempotence and perceptual image compression, two seemingly unrelated concepts in image coding. Idempotence refers to the stability of image compression when re-compressed, while perceptual image compression aims to preserve visual quality. The authors find that: 1. **Conditional Generative Model and Idempotence**: A conditional generative model-based image codec is idempotent, meaning that re-compressing the reconstructed image results in the same output. 2. **Unconditional Generative Model and Perceptual Quality**: An unconditional generative model with an idempotence constraint is equivalent to a conditional generative model-based image codec, achieving perceptual quality. Based on these findings, the authors propose a new paradigm for perceptual image compression by inverting an unconditional generative model with idempotence constraints. This approach does not require training new models and is theoretically equivalent to conditional generative codecs. Empirical results show that this method outperforms state-of-the-art perceptual image codecs in terms of Fréchet Inception Distance (FID) while maintaining low complexity during testing. The paper also discusses the practical implementation details, including the use of pre-trained models and different constraints for idempotence. It compares the proposed method with existing techniques and highlights its advantages in terms of perceptual quality and efficiency.