Active Learning for Conditional Generative Compressed Sensing
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 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.
Related
- Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing
- Minimax Rates for Conditional Generative Learning under Wasserstein Loss
- Superfast Spectral Compressed Sensing with Quadratic Convergence
- Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing
- Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization
BibTeX
@misc{delise2026active,
title = {{Active Learning for Conditional Generative Compressed Sensing}},
author = {Alexander DeLise and Nick Dexter},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.05435},
eprint = {2605.05435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.05435},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Active Learning for Conditional Generative Compressed Sensing
AU - Alexander DeLise
AU - Nick Dexter
PY - 2026
DA - 2026/11/08
PB - arXiv
DO - 10.48550/arxiv.2605.05435
UR - https://arxiv.org/abs/2605.05435
AB - 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.
ER -