They are not well characterized as single structures as has traditionally been the case, but rather as ensembles of structures with an ergodic probability distribution(Henzler-Wildman & Kern, 2007). Protein motion is required for myglobin to bind oxygen and move it around the body (Miller & Phillips, 2021). Drug discovery on protein kinases depends on characterizing kinase conforma-tional ensembles (Gough & Kalodimos, 2024). The search for druggable'cryptic pockets' requires understanding protein dynamics, and antibody design is deeply affected by conformational ensembles (Colombo, 2023). However, while machine learning (ML) methods for molecular structure prediction have experienced enormous success recently, ML methods for dynamics have yet to have similar impact. ML models for generating molecular ensembles are widely considered the'next frontier' (Bowman, 2024; Miller & Phillips, 2021; Zheng et al., 2023).

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, 2019] 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 (i.e., 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. VoxMol achieves comparable results to state of the art on unconditional 3D molecule generation while being simpler to train and faster to generate molecules.