Generative Decompression: Optimal Lossy Decoding Against Distribution Mismatch

TL;DR

The paper tackles lossy compression with a fixed encoder designed for a mismatched source, and shows that decoder-side Bayesian reconstruction using the true distribution—generative decompression—achieves lower distortion than standard centroid-based decoding. It formalizes the mismatched quantization problem, proves that the optimal decoder is the conditional expectation under the true distribution, and extends the approach to noisy channels via a soft-decoding rule that couples source priors with channel reliability. It further generalizes to task-oriented decoding and provides closed-form analyses for Gaussian and Laplace mismatches, plus thorough case studies (scalar and high-rate scalar quantization) and semantic classification experiments demonstrating substantial performance gains without altering the encoder. The framework illuminates when and how decoder-side priors close the distortion gap, quantifies the inefficiency of modular separation under mismatch, and offers practical pathways for adaptive, high-fidelity reconstruction in standardized, fixed-codecs. Overall, generative decompression enables robust, context-aware decoding in scenarios ranging from CSI feedback to semantic communication, with clear implications for 6G and beyond.

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.

Figures (7)

• Figure 1: Decoder-side gain vs. mean mismatch for Gaussian sources. Quantizers designed for $\mathcal{N}(0,1)$, evaluated on $\mathcal{N}(\mu_1, 1)$.
• Figure 2: Decoder-side gain vs. variance ratio for Gaussian sources. Quantizers designed for $\mathcal{N}(0,1)$, evaluated on $\mathcal{N}(0, \sigma_1^2)$.
• Figure 3: MSE distortion for 5 bits ($b=5$), comparing clean and augmented scenarios. The generative decoder closes a significant portion of the gap to the ideal benchmark despite the frozen encoder.
• Figure 4: Relative reconstruction gain vs. codebook size (bits) for varying target subset sizes $k$. Adaptation gains are highest for severe mismatch (small $k$) and low bit rates.
• Figure 5: Reconstruction gain comparison between clean and augmented scenarios at 8 bits. The relative benefit of generative adaptation is robust to domain shifts (augmentation).

Theorems & Definitions (6)

• Proposition 1
• Definition 1: Mismatch penalty factor
• Theorem 1: Perfect optimality at $N=1$
• Theorem 2: Distortion hierarchy
• Theorem 3: Asymptotic rate recovery
• Lemma 1: Asymmetry of Gaussian mismatch