Active Learning for Conditional Generative Compressed Sensing
For practitioners using generative models in compressed sensing, this work provides theoretical guarantees and practical insights on how to use prompts to design sampling distributions and improve recovery.
The paper studies conditional generative compressed sensing for image recovery from subsampled Fourier measurements using prompt-conditioned generative models. It proves stable recovery bounds showing prompt-matched Christoffel sampling retains near-optimal complexity, while prompt mismatch incurs a penalty, and experiments with Stable Diffusion confirm prompts reshape sampling distributions and influence recovery.
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 that prompts should be treated as design variables with distinct effects on sensing, approximation, and recovery.