# Active Diffusion Subsampling

arXiv: https://arxiv.org/abs/2406.14388 · HTML: https://mlsanity.com/paper/2406.14388/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 24 of its 58 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 24 of 24)

- [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)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [Deep Learning for Segmentation using an Open Large-Scale Dataset in 2D Echocardiography](https://mlsanity.com/paper/1908.06948/) (2019)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Latent Diffusion Energy-Based Model for Interpretable Text Modeling](https://mlsanity.com/paper/2206.05895/) (2022)
- [Experimental design for MRI by greedy policy search](https://mlsanity.com/paper/2010.16262/) (2020)
- [Dehazing Ultrasound using Diffusion Models](https://mlsanity.com/paper/2307.11204/) (2023)
- [Info-Greedy sequential adaptive compressed sensing](https://mlsanity.com/paper/1407.0731/) (2014)
- [Learning-based Compressive Subsampling](https://mlsanity.com/paper/1510.06188/) (2015)
- [Entropy, Information, and the Updating of Probabilities](https://mlsanity.com/paper/2107.04529/) (2021)
- [Accelerated Intravascular Ultrasound Imaging using Deep Reinforcement Learning](https://mlsanity.com/paper/2201.09522/) (2022)

## Built on by (most cited first, 8 of 8)

- [Sequential Posterior Sampling with Diffusion Models](https://mlsanity.com/paper/2409.05399/) (2024)
- [Active inference and deep generative modeling for cognitive ultrasound](https://mlsanity.com/paper/2410.13310/) (2024)
- [High Volume Rate 3D Ultrasound Reconstruction with Diffusion Models](https://mlsanity.com/paper/2505.22090/) (2025)
- [Online Feedback Efficient Active Target Discovery in Partially Observable Environments](https://mlsanity.com/paper/2505.06535/) (2025)
- [Flow-Based Generative Modeling for Optimizing Sampling Policies in Compressed Sensing Applications](https://mlsanity.com/paper/2606.00078/) (2026)
- [Active Data Acquisition with Side Information via Discrete Diffusion Priors](https://mlsanity.com/paper/2609.32252/) (2026)
- [GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors](https://mlsanity.com/paper/2609.34172/) (2026)
- [Deep Bayesian REFoCUS](https://mlsanity.com/paper/2610.03419/) (2026)

## Abstract (arXiv)

Subsampling is commonly used to mitigate costs associated with data acquisition, such as time or energy requirements, motivating the development of algorithms for estimating the fully-sampled signal of interest x from partially observed measurements y. In maximum entropy sampling, one selects measurement locations that are expected to have the highest entropy, so as to minimize uncertainty about x. This approach relies on an accurate model of the posterior distribution over future measurements, given the measurements observed so far. Recently, diffusion models have been shown to produce high-quality posterior samples of high-dimensional signals using guided diffusion. In this work, we propose Active Diffusion Subsampling (ADS), a method for designing intelligent subsampling masks using guided diffusion in which the model tracks a distribution of beliefs over the true state of x throughout the reverse diffusion process, progressively decreasing its uncertainty by actively choosing to acquire measurements with maximum expected entropy, ultimately producing the posterior distribution p(x mid y). ADS can be applied using pre-trained diffusion models for any subsampling rate, and does not require task-specific retraining - just the specification of a measurement model. Furthermore, the maximum entropy sampling policy employed by ADS is interpretable, enhancing transparency relative to existing methods using black-box policies. Code is available at https://active-diffusion-subsampling.github.io/.