Generative Decompression: Optimal Lossy Decoding Against Distribution Mismatch

TL;DR

This paper introduces generative decompression, an optimal decoding method for lossy compression under distribution mismatch, improving reconstruction quality by leveraging true source distribution information at the decoder.

Contribution

It formalizes the mismatched quantization problem, deriving a generative Bayesian decoding strategy that outperforms traditional methods and extends to noisy channels and task-oriented scenarios.

Findings

Generative decompression outperforms centroid decoding in experiments.

The approach reduces the performance gap to joint-optimization benchmarks.

It enables adaptive, high-fidelity reconstruction without changing the encoder.

Abstract

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.