# Rate-Distortion-Perception Theory for the Quadratic Wasserstein Space

arXiv: https://arxiv.org/abs/2504.17236 · HTML: https://mlsanity.com/paper/2504.17236/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 24 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [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)
- [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)
- [Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure](https://mlsanity.com/paper/2401.12207/) (2024)
- [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)

## Built on by (most cited first, 2 of 2)

- [TriDP-PTM: a three-stage distortion-perception tradeoff guides the pre-training model for radar cardiac sensing](https://mlsanity.com/paper/2605.25725/) (2026)
- [Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representation](https://mlsanity.com/paper/2607.17232/) (2026)

## Abstract (arXiv)

We establish a single-letter characterization of the fundamental distortion-rate-perception tradeoff with limited common randomness under the squared error distortion measure and the squared Wasserstein-2 perception measure. Moreover, it is shown that this single-letter characterization can be explicitly evaluated for the Gaussian source. Various notions of universal representation are also clarified.