# Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure

arXiv: https://arxiv.org/abs/2401.12207 · HTML: https://mlsanity.com/paper/2401.12207/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 17 of 17)

- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Conditional Probability Models for Deep Image Compression](https://mlsanity.com/paper/1801.04260/) (2018)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [Neural Video Compression using GANs for Detail Synthesis and Propagation](https://mlsanity.com/paper/2107.12038/) (2021)
- [Feedback Recurrent Autoencoder for Video Compression](https://mlsanity.com/paper/2004.04342/) (2020)
- [A coding theorem for the rate-distortion-perception function](https://mlsanity.com/paper/2104.13662/) (2021)
- [On the advantages of stochastic encoders](https://mlsanity.com/paper/2102.09270/) (2021)
- [On Perceptual Lossy Compression: The Cost of Perceptual Reconstruction and An Optimal Training Framework](https://mlsanity.com/paper/2106.02782/) (2021)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [Optimally Controllable Perceptual Lossy Compression](https://mlsanity.com/paper/2206.10082/) (2022)
- [Conditional Perceptual Quality Preserving Image Compression](https://mlsanity.com/paper/2308.08154/) (2023)

## Built on by (most cited first, 8 of 8)

- [Output-Constrained Lossy Source Coding With Application to Rate-Distortion-Perception Theory](https://mlsanity.com/paper/2403.14849/) (2024)
- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)
- [Optimal Neural Compressors for the Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/2503.17558/) (2025)
- [Rate-Distortion-Perception Theory for the Quadratic Wasserstein Space](https://mlsanity.com/paper/2504.17236/) (2025)
- [Constrained Gaussian Wasserstein Optimal Transport with Commutative Covariance Matrices](https://mlsanity.com/paper/2503.03744/) (2025)
- [Training-Free Rate-Distortion-Perception Traversal With Diffusion](https://mlsanity.com/paper/2603.04005/) (2026)
- [A Synonymous Variational Perspective on the Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/2604.14603/) (2026)
- [TriDP-PTM: a three-stage distortion-perception tradeoff guides the pre-training model for radar cardiac sensing](https://mlsanity.com/paper/2605.25725/) (2026)

## Abstract (arXiv)

This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output, first proposed by Mentzer et al. We consider the case when there is no shared randomness between the encoder and the decoder and derive a single-letter characterization of the RDP function for the case of discrete memoryless sources. This is in contrast to the marginal-distribution metric case (introduced by Blau and Michaeli), whose RDP characterization remains open when there is no shared randomness. The achievability scheme is based on lossy source coding with a posterior reference map. For the case of continuous valued sources under the squared error distortion measure and the squared quadratic Wasserstein perception measure, we also derive a single-letter characterization and show that the decoder can be restricted to a noise-adding mechanism. Interestingly, the RDP function characterized for the case of zero perception loss coincides with that of the marginal metric, and further zero perception loss can be achieved with a 3-dB penalty in minimum distortion. Finally we specialize to the case of Gaussian sources, and derive the RDP function for Gaussian vector case and propose a reverse water-filling type solution. We also partially characterize the RDP function for a mixture of Gaussian vector sources.