End-To-End Latent Variational Diffusion Models for Inverse Problems in
  High Energy Physics
Alexander Shmakov Kevin Greif Michael Fenton Aishik Ghosh Pierre Baldi Daniel Whiteson
High-energy collisions at the Large Hadron Collider (LHC) provide valuable
insights into open questions in particle physics. However, detector effects
must be corrected before measurements can be compared to certain theoretical
predictions or measurements from other detectors. Methods to solve this
\textit{inverse problem} of mapping detector observations to theoretical
quantities of the underlying collision are essential parts of many physics
analyses at the LHC. We investigate and compare various generative deep
learning methods to approximate this inverse mapping. We introduce a novel
unified architecture, termed latent variation diffusion models, which combines
the latent learning of cutting-edge generative art approaches with an
end-to-end variational framework. We demonstrate the effectiveness of this
approach for reconstructing global distributions of theoretical kinematic
quantities, as well as for ensuring the adherence of the learned posterior
distributions to known physics constraints. Our unified approach achieves a
distribution-free distance to the truth of over 20 times less than non-latent
state-of-the-art baseline and 3 times less than traditional latent diffusion
models.