# Generative Decompression: Optimal Lossy Decoding Against Distribution Mismatch

arXiv: https://arxiv.org/abs/2602.03505 · HTML: https://mlsanity.com/paper/2602.03505/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications](https://mlsanity.com/paper/2207.09353/) (2022)
- [6G Networks: Beyond Shannon Towards Semantic and Goal-Oriented Communications](https://mlsanity.com/paper/2011.14844/) (2020)
- [Semantic Communications: Principles and Challenges](https://mlsanity.com/paper/2201.01389/) (2021)
- [Deep Generative Models for Distribution-Preserving Lossy Compression](https://mlsanity.com/paper/1805.11057/) (2018)
- [Joint Source-Channel Coding: Fundamentals and Recent Progress in Practical Designs](https://mlsanity.com/paper/2409.17557/) (2024)
- [Context-Aware Semantic Inpainting](https://mlsanity.com/paper/1712.07778/) (2017)
- [A Bias-Variance Decomposition for Ensembles over Multiple Synthetic Datasets](https://mlsanity.com/paper/2402.03985/) (2024)
- [Rateless Joint Source-Channel Coding, and a Blueprint for 6G Semantic Communications System Design](https://mlsanity.com/paper/2502.06095/) (2025)
- [Generative Decoding of Compressed CSI for MIMO Precoding Design](https://mlsanity.com/paper/2511.07783/) (2025)

## Abstract (arXiv)

This paper addresses optimal decoding strategies in lossy compression where the assumed distribution for compressor design mismatches the actual (true) distribution of the source. This problem has immediate relevance in standardized communication systems where the decoder acquires side information or priors about the true distribution that are unavailable to the fixed encoder. We formally define the mismatched quantization problem, demonstrating that the optimal reconstruction rule, termed generative decompression, aligns with classical Bayesian estimation by taking the conditional expectation under the true distribution given the quantization indices and adapting it to fixed-encoder constraints. This strategy effectively performs a generative Bayesian correction on the decoder side, strictly outperforming the conventional centroid rule. We extend this framework to transmission over noisy channels, deriving a robust soft-decoding rule that quantifies the inefficiency of standard modular source--channel separation architectures under mismatch. Furthermore, we generalize the approach to task-oriented decoding, showing that the optimal strategy shifts from conditional mean estimation to maximum a posteriori (MAP) detection. Experimental results on Gaussian sources and deep-learning-based semantic classification demonstrate that generative decompression closes a vast majority of the performance gap to the ideal joint-optimization benchmark, enabling adaptive, high-fidelity reconstruction without modifying the encoder.