  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 performing active subsampling 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
choosing to acquire measurements with maximum expected entropy, and ultimately
generating the posterior distribution $p(x | y)$. 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. Experimentally, we show that ADS outperforms fixed sampling
strategies, and study an application of ADS in Magnetic Resonance Imaging
acceleration using the fastMRI dataset, finding that ADS performs competitively
with supervised methods. Code available at
https://active-diffusion-subsampling.github.io/.
