  Protein-ligand binding prediction is a fundamental problem in AI-driven drug
discovery. Prior work focused on supervised learning methods using a large set
of binding affinity data for small molecules, but it is hard to apply the same
strategy to other drug classes like antibodies as labelled data is limited. In
this paper, we explore unsupervised approaches and reformulate binding energy
prediction as a generative modeling task. Specifically, we train an
energy-based model on a set of unlabelled protein-ligand complexes using SE(3)
denoising score matching and interpret its log-likelihood as binding affinity.
Our key contribution is a new equivariant rotation prediction network called
Neural Euler's Rotation Equations (NERE) for SE(3) score matching. It predicts
a rotation by modeling the force and torque between protein and ligand atoms,
where the force is defined as the gradient of an energy function with respect
to atom coordinates. We evaluate NERE on protein-ligand and antibody-antigen
binding affinity prediction benchmarks. Our model outperforms all unsupervised
baselines (physics-based and statistical potentials) and matches supervised
learning methods in the antibody case.
