We presents VoxBind, a new score-based generative model for 3D molecules conditioned on protein structures. Our approach represents molecules as 3D atomic density grids and leverages a 3D voxel-denoising network for learning and generation. We extend the neural empirical Bayes formalism (Saremi & Hyvärinen, 2019) to the conditional setting and generate structure-conditioned molecules with a two-step procedure: (i) sample noisy molecules from the Gaussian-smoothed conditional distribution with underdamped Langevin MCMC using the learned score function and (ii) estimate clean molecules from the noisy samples with single-step denoising. Compared to the current state of the art, our model is simpler to train, significantly faster to sample from, and achieves better results on extensive in silico benchmarks—the generated molecules are more diverse, exhibit fewer steric clashes, and bind with higher affinity to protein pockets.

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 (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.

The analysis of single-cell genomics data presents several statistical challenges, and extensive efforts have been made to produce methods for the analysis of this data that impute missing values, address sampling issues and quantify and correct for noise. In spite of such efforts, no consensus on best practices has been established and all current approaches vary substantially based on the available data and empirical tests. The k-Nearest Neighbor Graph (kNN-G) is often used to infer the identities of, and relationships between, cells and is the basis of many widely used dimensionality-reduction and projection methods. The kNN-G has also been the basis for imputation methods using, e.g., neighbor averaging and graph diffusion. However, due to the lack of an agreed-upon optimal objective function for choosing hyperparameters, these methods tend to oversmooth data, thereby resulting in a loss of information with regard to cell identity and the specific gene-to-gene patterns underlying regulatory mechanisms. In this paper, we investigate the tuning of kNN- and diffusion-based denoising methods with a novel non-stochastic method for optimally preserving biologically relevant informative variance in single-cell data. The framework, Denoising Expression data with a Weighted Affinity Kernel and Self-Supervision (DEWÄKSS), uses a self-supervised technique to tune its parameters. We demonstrate that denoising with optimal parameters selected by our objective function (i) is robust to preprocessing methods using data from established benchmarks, (ii) disentangles cellular identity and maintains robust clusters over dimension-reduction methods, (iii) maintains variance along several expression dimensions, unlike previous heuristic-based methods that tend to oversmooth data variance, and (iv) rarely involves diffusion but rather uses a fixed weighted kNN graph for denoising. Together, these findings provide a new understanding of kNN- and diffusion-based denoising methods. Code and example data for DEWÄKSS is available at https://gitlab.com/Xparx/dewakss/-/tree/Tjarnberg2020branch.