Active Diffusion Subsampling

TMLR Paper3687 Authors

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 dif-
fusion 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 pos-
terior 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 through designing informative subsampling masks,
ADS significantly improves reconstruction quality compared to fixed sampling strategies on
the MNIST and CelebA datasets, as measured by standard image quality metrics, includ-
ing PSNR, SSIM, and LPIPS. Furthermore, on the task of Magnetic Resonance Imaging
acceleration, we find that ADS performs competitively with existing supervised methods in
reconstruction quality while using a more interpretable acquisition scheme design procedure.
Code is available at https://active-diffusion-subsampling.github.io/.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission: Reference linking errors have now been resolved.

Assigned Action Editor: ~David_Rügamer1

Submission Number: 3687