Modern single-image super-resolution (SISR) models deliver photo-realistic results at the scale factors on which they are trained, but collapse when asked to magnify far beyond that regime. We address this scalability bottleneck with Chain-of-Zoom (CoZ), a model-agnostic framework that factorizes SISR into an autoregressive chain of intermediate scale-states with multi-scale-aware prompts. CoZ repeatedly re-uses a backbone SR model, decomposing the conditional probability into tractable sub-problems to achieve extreme resolutions without additional training. Because visual cues diminish at high magnifications, we augment each zoom step with multi-scale-aware text prompts generated by a vision-language model (VLM). The prompt extractor itself is fine-tuned using Generalized Reward Policy Optimization (GRPO) with a critic VLM, aligning text guidance towards human preference. Experiments show that a standard 4 diffusion SR model wrapped in CoZ attains beyond 256 enlargement with high perceptual quality and fidelity.

In addition to solving (1), we also wish topreserve privacyfor the people who contributed to the dataset Z.

Numerical experiments are conducted tosupport our theoretical results.

Recently, diffusion models havebeen used to solvevarious inverse problems in anunsupervised manner withappropriate modifications tothesampling process.

Smooth convex optimization problems over polytopes are an important class of problems that appear in many settings, such as low-rank matrix completion [1],structured supervised learning [2,3],electrical flowsovergraphs [4],video co-localization in computer vision [5], traffic assignment problems [6], and submodular function minimization [7].