Active Learning for Conditional Generative Compressed Sensing

TL;DR

This paper explores how prompt-conditioned generative models can improve image recovery in compressed sensing, analyzing the effects of prompts on sampling and recovery quality.

Contribution

It introduces a framework separating sampling and recovery prompts, providing theoretical bounds and experimental evidence for prompt influence in generative compressed sensing.

Findings

Prompt-matched Christoffel sampling retains optimal complexity.

Prompt mismatch introduces a compatibility penalty.

Prompts significantly influence sampling distribution and image recovery.

Abstract

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.