Generative Decompression: Optimal Lossy Decoding Against Distribution Mismatch

2026-02-03

AI Summary

This work addresses the suboptimal reconstruction in lossy compression caused by the mismatch between the encoder’s assumed source distribution and the true data distribution. To mitigate this issue without modifying the encoder, the authors propose a generative decompression framework that leverages prior knowledge of the true source distribution at the decoder. By employing Bayesian estimation and conditional expectation, the method achieves optimal reconstruction under the fixed encoder constraint. This study is the first to introduce Bayes-optimal decoding into mismatched compression scenarios and extends the approach to noisy channels and task-oriented compression. The framework integrates Gaussian source modeling, maximum a posteriori detection, and deep semantic classification, significantly narrowing the performance gap with jointly optimized benchmarks while enabling high-fidelity, adaptive reconstruction.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• distribution mismatch
• lossy compression
• optimal decoding
• generative decompression
• quantization

Innovation

• generative decompression
• distribution mismatch
• Bayesian estimation
• task-oriented decoding
• soft-decoding