Active Diffusion Subsampling

TL;DR

Active Diffusion Subsampling (ADS) leverages guided diffusion models to intelligently select measurement locations by actively reducing uncertainty, enabling high-quality posterior estimation without task-specific retraining and improving transparency over black-box methods.

Contribution

ADS introduces a novel active subsampling method using guided diffusion models that tracks belief distributions and selects measurements based on maximum entropy, without requiring retraining.

Findings

Effective in reducing uncertainty during subsampling

Compatible with pre-trained diffusion models

Provides interpretable measurement selection policy

Abstract

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/.