# A Synonymous Variational Perspective on the Rate-Distortion-Perception Tradeoff

arXiv: https://arxiv.org/abs/2604.14603 · HTML: https://mlsanity.com/paper/2604.14603/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 19 of 19)

- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [One-Shot Free-View Neural Talking-Head Synthesis for Video Conferencing](https://mlsanity.com/paper/2011.15126/) (2020)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Speech Resynthesis from Discrete Disentangled Self-Supervised Representations](https://mlsanity.com/paper/2104.00355/) (2021)
- [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)
- [Towards image compression with perfect realism at ultra-low bitrates](https://mlsanity.com/paper/2310.10325/) (2023)
- [Improving Statistical Fidelity for Neural Image Compression with Implicit Local Likelihood Models](https://mlsanity.com/paper/2301.11189/) (2023)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [Perceptual Learned Video Compression with Recurrent Conditional GAN](https://mlsanity.com/paper/2109.03082/) (2021)
- [A coding theorem for the rate-distortion-perception function](https://mlsanity.com/paper/2104.13662/) (2021)
- [Generative Latent Coding for Ultra-Low Bitrate Image Compression](https://mlsanity.com/paper/2512.20194/) (2025)
- [Diffusion-based Perceptual Neural Video Compression with Temporal Diffusion Information Reuse](https://mlsanity.com/paper/2501.13528/) (2025)
- [Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure](https://mlsanity.com/paper/2401.12207/) (2024)
- [Computation of Rate-Distortion-Perception Function under f-Divergence Perception Constraints](https://mlsanity.com/paper/2305.04604/) (2023)
- [Synonymous Variational Inference for Perceptual Image Compression](https://mlsanity.com/paper/2505.22438/) (2025)

## Abstract (arXiv)

The fundamental limit of natural signal compression has traditionally been characterized by classical rate-distortion (RD) theory through the tradeoff between coding rate and reconstruction distortion, while the rate-distortion-perception (RDP) framework introduces a divergence-based measure of perceptual quality as a modeling principle, leaving its theoretical origin unclear. In this paper, motivated by a synonymity-based semantic information perspective, we reformulate perceptual reconstruction as recovering any admissible sample within an ideal synonymous set (synset) associated with the source, rather than the source sample itself, and establish a synonymous source coding architecture. On this basis, we develop a synonymous variational inference (SVI) analysis framework with a synonymous variational lower bound (SVLBO) for tractable analysis of synset-oriented compression. Within this framework, we establish a synonymity-perception consistency principle, showing that optimal identification of semantic information is theoretically consistent with perceptual optimization. Based on this result, we further derive a tight-bound synonymous source coding rate characterization and show that its Jensen-limit relaxation leads to a synonymous rate-distortion-perception form for practical optimization. These analytical results show that the distributional divergence term arises naturally from the synset-based reconstruction objective, clarify its compatibility with existing RDP formulations and classical RD theory, and suggest the potential advantages of synonymous source coding.