# Active Learning for Conditional Generative Compressed Sensing

arXiv: https://arxiv.org/abs/2605.05435 · HTML: https://mlsanity.com/paper/2605.05435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [Robust Compressed Sensing using Generative Models](https://mlsanity.com/paper/2006.09461/) (2020)
- [Regularization by Texts for Latent Diffusion Inverse Solvers](https://mlsanity.com/paper/2311.15658/) (2023)
- [Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models](https://mlsanity.com/paper/1908.10744/) (2019)
- [Fourier Sparse Leverage Scores and Approximate Kernel Learning](https://mlsanity.com/paper/2006.07340/) (2020)
- [Leveraged volume sampling for linear regression](https://mlsanity.com/paper/1802.06749/) (2018)
- [A Universal Sampling Method for Reconstructing Signals with Simple Fourier Transforms](https://mlsanity.com/paper/1812.08723/) (2018)
- [CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions](https://mlsanity.com/paper/2306.00945/) (2023)
- [ContextMRI: Enhancing Compressed Sensing MRI through Metadata Conditioning](https://mlsanity.com/paper/2501.04284/) (2025)
- [Lower Bounds for Compressed Sensing with Generative Models](https://mlsanity.com/paper/1912.02938/) (2019)
- [A coherence parameter characterizing generative compressed sensing with Fourier measurements](https://mlsanity.com/paper/2207.09340/) (2022)
- [A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing](https://mlsanity.com/paper/2310.03758/) (2023)
- [Model-adapted Fourier sampling for generative compressed sensing](https://mlsanity.com/paper/2310.04984/) (2023)
- [Optimal sampling for least-squares approximation](https://mlsanity.com/paper/2409.02342/) (2024)
- [A statistical perspective of sampling scores for linear regression](https://mlsanity.com/paper/1507.05870/) (2015)
- [Beyond Independent Measurements: General Compressed Sensing with GNN Application](https://mlsanity.com/paper/2111.00327/) (2021)
- [Generalized Leverage Scores: Geometric Interpretation and Applications](https://mlsanity.com/paper/2206.08054/) (2022)
- [Denoising guarantees for optimized sampling schemes in compressed sensing](https://mlsanity.com/paper/2504.01046/) (2025)

## Abstract (arXiv)

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.