Bayes' Theorem allows a program to infer the probabilities of likely causes from the probabilities of their effects, when what it is given are the probabilities of effects, given the causes.
For example, in personalized medical diagnostics, a model is built based on historical data to facilitate an optimal treatment for a new patient (Bica et al., 2021).
Recent advancements in solving Bayesian inverse problems have spotlighted de-noising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to sample.