# Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling

arXiv: https://arxiv.org/abs/2407.08256 · HTML: https://mlsanity.com/paper/2407.08256/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 81 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 30 of 54)

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Models](https://mlsanity.com/paper/2402.17177/) (2024)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [VideoFusion: Decomposed Diffusion Models for High-Quality Video Generation](https://mlsanity.com/paper/2303.08320/) (2023)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)

## Built on by (most cited first, 13 of 13)

- [SILO: Solving Inverse Problems with Latent Operators](https://mlsanity.com/paper/2501.11746/) (2025)
- [InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems](https://mlsanity.com/paper/2504.01689/) (2025)
- [PSC: Posterior Sampling-Based Compression](https://mlsanity.com/paper/2407.09896/) (2024)
- [Diffusion Active Learning: Towards Data-Driven Experimental Design in Computed Tomography](https://mlsanity.com/paper/2504.03491/) (2025)
- [Dynamic Angle Selection in X-Ray CT: A Reinforcement Learning Approach to Optimal Stopping](https://mlsanity.com/paper/2503.12688/) (2025)
- [Sampling Innovation-Based Adaptive Compressive Sensing](https://mlsanity.com/paper/2503.13241/) (2025)
- [NoiseRater: Meta-Learned Noise Valuation for Diffusion Model Training](https://mlsanity.com/paper/2605.08144/) (2026)
- [Anatomical Token Uncertainty for Transformer-Guided Active MRI Acquisition](https://mlsanity.com/paper/2603.21806/) (2026)
- [Stage-wise Distortion-Perception Traversal in Zero-shot Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2605.28711/) (2026)
- [Classification-oriented adaptive sensing via posterior sampling](https://mlsanity.com/paper/2609.21812/) (2026)
- [How Many Posterior Samples? Calibrated Stopping for Adaptive Sensing](https://mlsanity.com/paper/2609.21813/) (2026)
- [GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors](https://mlsanity.com/paper/2609.34172/) (2026)
- [H-DDCM: Hadamard Codebooks for Fast Generative Image and Video Compression](https://mlsanity.com/paper/2610.18125/) (2026)

## Abstract (arXiv)

Compressed Sensing (CS) facilitates rapid image acquisition by selecting a small subset of measurements sufficient for high-fidelity reconstruction. Adaptive CS seeks to further enhance this process by dynamically choosing future measurements based on information gleaned from data that is already acquired. However, many existing frameworks are often tailored to specific tasks and require intricate training procedures. We propose AdaSense, a novel Adaptive CS approach that leverages zero-shot posterior sampling with pre-trained diffusion models. By sequentially sampling from the posterior distribution, we can quantify the uncertainty of each possible future linear measurement throughout the acquisition process. AdaSense eliminates the need for additional training and boasts seamless adaptation to diverse domains with minimal tuning requirements. Our experiments demonstrate the effectiveness of AdaSense in reconstructing facial images from a small number of measurements. Furthermore, we apply AdaSense for active acquisition of medical images in the domains of magnetic resonance imaging (MRI) and computed tomography (CT), highlighting its potential for tangible real-world acceleration.