# Optimally Controllable Perceptual Lossy Compression

arXiv: https://arxiv.org/abs/2206.10082 · HTML: https://mlsanity.com/paper/2206.10082/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 30 of 37)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Semantic Scene Completion from a Single Depth Image](https://mlsanity.com/paper/1611.08974/) (2016)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Photographic Image Synthesis with Cascaded Refinement Networks](https://mlsanity.com/paper/1707.09405/) (2017)
- [Generating Images with Perceptual Similarity Metrics based on Deep Networks](https://mlsanity.com/paper/1602.02644/) (2016)
- [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)
- [Full Resolution Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1608.05148/) (2016)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [The 2018 PIRM Challenge on Perceptual Image Super-resolution](https://mlsanity.com/paper/1809.07517/) (2018)
- [Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations](https://mlsanity.com/paper/1704.00648/) (2017)
- [Learning a No-Reference Quality Metric for Single-Image Super-Resolution](https://mlsanity.com/paper/1612.05890/) (2016)
- [Conditional Probability Models for Deep Image Compression](https://mlsanity.com/paper/1801.04260/) (2018)
- [Real-Time Adaptive Image Compression](https://mlsanity.com/paper/1705.05823/) (2017)
- [Learning Convolutional Networks for Content-weighted Image Compression](https://mlsanity.com/paper/1703.10553/) (2017)
- [Deep Generative Models for Distribution-Preserving Lossy Compression](https://mlsanity.com/paper/1805.11057/) (2018)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [Soft then Hard: Rethinking the Quantization in Neural Image Compression](https://mlsanity.com/paper/2104.05168/) (2021)

## Built on by (most cited first, 13 of 13)

- [StableCodec: Taming One-Step Diffusion for Extreme Image Compression](https://mlsanity.com/paper/2506.21977/) (2025)
- [Idempotence and Perceptual Image Compression](https://mlsanity.com/paper/2401.08920/) (2024)
- [EGIC: Enhanced Low-Bit-Rate Generative Image Compression Guided by Semantic Segmentation](https://mlsanity.com/paper/2309.03244/) (2023)
- [Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure](https://mlsanity.com/paper/2401.12207/) (2024)
- [Ultra-Low Bitrate Perceptual Image Compression with Shallow Encoder](https://mlsanity.com/paper/2512.12229/) (2025)
- [Conditional Perceptual Quality Preserving Image Compression](https://mlsanity.com/paper/2308.08154/) (2023)
- [Dual-Representation Image Compression at Ultra-Low Bitrates via Explicit Semantics and Implicit Textures](https://mlsanity.com/paper/2602.05213/) (2026)
- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)
- [Rate-Distortion-Perception Theory for the Quadratic Wasserstein Space](https://mlsanity.com/paper/2504.17236/) (2025)
- [Characterization of the Distortion-Perception Tradeoff for Finite Channels with Arbitrary Metrics](https://mlsanity.com/paper/2402.02265/) (2024)
- [Advances in Diffusion-Based Generative Compression](https://mlsanity.com/paper/2601.18932/) (2026)
- [Fast Training-free Perceptual Image Compression](https://mlsanity.com/paper/2506.16102/) (2025)
- [FLM: Frequency-Aware Language Models for Generative Image Compression](https://mlsanity.com/paper/2608.28687/) (2026)

## Abstract (arXiv)

Recent studies in lossy compression show that distortion and perceptual quality are at odds with each other, which put forward the tradeoff between distortion and perception (D-P). Intuitively, to attain different perceptual quality, different decoders have to be trained. In this paper, we present a nontrivial finding that only two decoders are sufficient for optimally achieving arbitrary (an infinite number of different) D-P tradeoff. We prove that arbitrary points of the D-P tradeoff bound can be achieved by a simple linear interpolation between the outputs of a minimum MSE decoder and a specifically constructed perfect perceptual decoder. Meanwhile, the perceptual quality (in terms of the squared Wasserstein-2 distance metric) can be quantitatively controlled by the interpolation factor. Furthermore, to construct a perfect perceptual decoder, we propose two theoretically optimal training frameworks. The new frameworks are different from the distortion-plus-adversarial loss based heuristic framework widely used in existing methods, which are not only theoretically optimal but also can yield state-of-the-art performance in practical perceptual decoding. Finally, we validate our theoretical finding and demonstrate the superiority of our frameworks via experiments. Code is available at: https://github.com/ZeyuYan/Controllable-Perceptual-Compression