  We propose a new score-based approach to generate 3D molecules represented as
atomic densities on regular grids. First, we train a denoising neural network
that learns to map from a smooth distribution of noisy molecules to the
distribution of real molecules. Then, we follow the neural empirical Bayes
framework (Saremi and Hyvarinen, 19) and generate molecules in two steps: (i)
sample noisy density grids from a smooth distribution via underdamped Langevin
Markov chain Monte Carlo, and (ii) recover the "clean" molecule by denoising
the noisy grid with a single step. Our method, VoxMol, generates molecules in a
fundamentally different way than the current state of the art (ie, diffusion
models applied to atom point clouds). It differs in terms of the data
representation, the noise model, the network architecture and the generative
modeling algorithm. Our experiments show that VoxMol captures the distribution
of drug-like molecules better than state of the art, while being faster to
generate samples.
