Active Diffusion Subsampling

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/.