PerQ: Inverse Generative Modeling for Neural Image Compression via Quantization Error Compensation

Neural image codecs face a fundamental trade-off between pixel fidelity and perceptual quality. Distortion-optimized codecs preserve pixel-wise fidelity but produce blurred reconstructions at low bitrates, whereas generative codecs leverage learned priors to improve perceptual quality but tend to exhibit saturating PSNR at higher bitrates and require separate models for different bitrate targets. We propose PerQ, which reframes perceptual reconstruction as inverse generative modeling with bounded support. Specifically, we define the quantization cell as the set of latents that yield the same transmitted symbols and derive a transport bound showing that reconstructions from this cell remain within a rate-determined radius of the codec output. This motivates performing generative reconstruction within the codec-induced quantization cell, rather than sampling from an unconstrained image prior. PerQ implements this principle by attaching a rate-conditioned flow-matching compensator to a frozen, multi-rate distortion-optimized backbone, enabling perceptual enhancement while preserving the backbone's coding performance. Experiments on Kodak and CLIC2020 show that PerQ achieves perceptual performance comparable to generative codecs such as MS-ILLM in LPIPS and FID, while maintaining competitive PSNR relative to distortion-optimized codecs such as ELIC. A single model checkpoint supports a wide bitrate range with fast decoding, and the compensator provides consistent gains across three different backbones. The implementation is available at https://jasminepp.github.io/PerQ/.