Title: MolEBM: Molecule Generation and Design by Latent Space Energy-Based Modeling. Abstract: Generation of molecules with desired chemical and biological properties such as high drug-likeness, high binding affinity to target proteins, is critical in drug discovery. In this paper, we propose a probabilistic generative model to capture the joint distribution of molecules and their properties. Our model assumes an energy-based model (EBM) in the latent space. Given the latent vector sampled from the latent space EBM, both molecules and molecular properties are conditionally sampled via a top-down molecule generator model and a property regression model respectively. The EBM in a low dimensional latent space allows our model to capture complex chemical rules implicitly but efficiently and effectively. Due to the joint modeling with chemical properties, molecule design can be conveniently and naturally achieved by conditional sampling from our learned model given desired properties, in both single-objective and multi-objective optimization settings. The latent space EBM, top-down molecule generator, and property regression model are learned jointly by maximum likelihood, while optimization of properties is accomplished by gradual shifting of the model distribution towards the region supported by molecules with high property values. Our experiments show that our model outperforms state-of-the-art models on various molecule design tasks. 