Learned image compression (LIC) has shown great promise for achieving high rate-distortion performance. However, current LIC methods are often limited in their capability to model the complex correlation structures inherent in natural images, particularly the entanglement of invariant global structures with transient local textures within a single monolithic representation. This limitation precipitates severe geometric deformation at low bitrates. To address this, we introduce a framework predicated on functional decomposition, which we term Deeply-Conditioned Image Compression via self-generated priors (DCIC-sgp). Our central idea is to first encode a potent, self-generated prior to encapsulate the image's structural backbone. This prior is subsequently utilized not as mere side-information, but to holistically modulate the entire compression pipeline. This deep conditioning, most critically of the analysis transform, liberates it to dedicate its representational capacity to the residual, high-entropy details. This hierarchical, dependency-driven approach achieves an effective disentanglement of information streams. Our extensive experiments validate this assertion; visual analysis demonstrates that our method substantially mitigates the geometric deformation artifacts that plague conventional codecs at low bitrates. Quantitatively, our framework establishes highly competitive performance, achieving significant BD-rate reductions of 14.4%, 15.7%, and 15.1% against the VVC test model VTM-12.1 on the Kodak, CLIC, and Tecnick datasets.

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