← 研踪 PaperTrailarXiv:2605.05435 · v2
Active Learning for Conditional Generative Compressed Sensing
首次提交 2026-05-07 04:50
版本更新 2026-11-08 11:49
雷达观测 2026-11-10 12:16
摘要
Generative compressed sensing uses the range of a pretrained generator as a nonlinear model for recovering structured signals from limited measurements. We study a conditional version of this problem for image recovery from subsampled Fourier measurements using prompt-conditioned generative models. Our framework separates two roles of conditioning: the prompt used to design the sampling distribution and the prompt used to define the recovery model. For ReLU and Lipschitz conditional generators, we prove stable recovery bounds showing that prompt-matched Christoffel sampling retains the same Christoffel complexity constant as existing near-optimal generative compressed sensing theory, while prompt mismatch incurs an explicit compatibility penalty. Experiments with Stable Diffusion show that prompts meaningfully reshape Christoffel sampling distributions and influence image recovery. Overall, our results suggest treating prompts as design variables for sensing, approximation, and recovery, opening new directions for the practical use of conditional generative models in compressed sensing, where conditioning, sampling, and optimization must be considered jointly.
作者备注：45 pages, including appendices. Accepted at NeurIPS 2026; camera-ready version
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v2 · 2026-11-08 11:49 · 最新观测版本
Active Learning for Conditional Generative Compressed Sensing
Generative compressed sensing uses the range of a pretrained generator as a nonlinear model for recovering structured signals from limited measurements. We study a conditional version of this problem for image recovery from subsampled Fourier measurements using prompt-conditioned generative models. Our framework separates two roles of conditioning: the prompt used to design the sampling distribution and the prompt used to define the recovery model. For ReLU and Lipschitz conditional generators, we prove stable recovery bounds showing that prompt-matched Christoffel sampling retains the same Christoffel complexity constant as existing near-optimal generative compressed sensing theory, while prompt mismatch incurs an explicit compatibility penalty. Experiments with Stable Diffusion show that prompts meaningfully reshape Christoffel sampling distributions and influence image recovery. Overall, our results suggest treating prompts as design variables for sensing, approximation, and recovery, opening new directions for the practical use of conditional generative models in compressed sensing, where conditioning, sampling, and optimization must be considered jointly.
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