Active Learning for Conditional Generative Compressed Sensing

Numerous modern applications in signal processing and medical imaging necessitate acquiring high-dimensional signals under tight resource constraints. Traditional sampling theory suggests that accurate signal reconstruction requires a number of measurements proportional to the signal's ambient dimension, a requirement often too expensive or impractical. Compressed sensing challenges this notion by demonstrating that sparse signals can be recovered with fewer measurements, provided the measurement operator meets certain conditions. This proof-of-concept study presents a task-aware flow-based generative framework -- a reformulation of the conventional Flow Matching training paradigm with a flow model trained to optimize subsampling in compressed sensing applications. We establish the fundamental feasibility of the proposed framework of learning subsampling masks that substantially enhance the performance of compressed sensing for image classification, image reconstruction, and MRI acceleration. For the image reconstruction task, our method demonstrated state-of-the-art performance, achieving Peak Signal-to-Noise Ratio of 25.17 dB at the subsampling rate of 5% on the CelebA dataset and 29.24 dB when reconstructing $8\times$ accelerated MRI measurements (fastMRI dataset) with the minimal computational overhead. These results highlight the effectiveness of task-conditioning within generative flow models and reveal a promising direction for representation learning strategies. Overall, the proposed framework offers a unified, flexible approach to designing data- and task-driven sensing schemes that can be potentially adapted to a broad range of inverse problems.

Diffusion models have become a dominant paradigm for conditional image generation, yet existing approaches generally follow two directions: task-specific designs that can improve performance but limit generalization, and training-free loss guidance that compresses rich conditions into scalar objectives and applies stepwise guidance, leading to information bottlenecks and error accumulation along the sampling trajectory. Given the urgent need for an effective unified framework across diverse conditional image generation tasks, we propose Data Injection and Contrastive Trajectory Refinement (DICT), a training-free inference method that enhances conditional image generation without introducing task-dependent architectures. DICT introduces Data Injection, where noise-perturbed conditional signals are integrated into early denoising stages; by performing guided denoising on these injected signals, DICT adaptively selects and distills task-salient information from the raw condition, effectively preserving spatial richness and ensuring precise condition-to-generation alignment. Furthermore, DICT applies Contrastive Trajectory Refinement across adjacent denoising states, enabling pairwise comparisons that progressively improve sample quality. These designs keep inference simple while improving cross-task transfer under a unified diffusion formulation. Extensive experiments on conditional image generation tasks (e.g., style transfer, image super-resolution, and image deblurring) show consistent gains in fidelity and perceptual quality over representative task-specific and loss-guided baselines.

Generative models learn the statistical properties of their training data, so high-quality generation depends on clean and representative datasets. In scientific imaging, acquisition often yields noisy measurements, while collecting clean references can be costly, impractical or even unattainable. Training directly on these measurements results in a model that reproduces the corrupted data. This can be circumvented by learning the clean population distribution directly from the noisy data. Conditional flow matching (CFM) combines a simple regression objective with stable training, efficient sampling, and strong image-generation performance, making it a natural framework for this setting. We introduce Noise-Robust Conditional Flow Matching (NR-CFM), an unconditional generator that learns from one corrupted observation per image. NR-CFM provides a closed-form clean endpoint correction for additive white Gaussian noise and learns a data-driven correction for general Gaussian corruptions with more complex covariance structure. Across the evaluated corruption settings, NR-CFM outperforms NR-GAN in most cases and remains competitive with Ambient Diffusion in the high-noise regime. We further evaluate NR-CFM on scientific data at signal-to-noise ratios as low as $0.001$, where it generates plausible particle images from severely corrupted measurements.