Machine learning already enables the discovery of new materials by providing rapid predictions of properties to complement slower calculations and experiments. However, a persistent criticism of machine learning enabled materials discovery is that new materials are very similar, both chemically and structurally, to previously known materials. This begs the question “Can machine learning ever learn new chemistries and families of materials that differ from those present in the training data?” In this talk, I will describe two important tools we are developing to truly move beyond screening to actual discovery. First, I will describe new generative machine learning approaches that can be used to generate structures that do not yet exist, but are likely to. I will compare generative models including variational autoencoders, generative adversarial networks, and diffusion models which have become standard in machine learning for images. I will describe the unique challenges that we face when using tools of this nature to generate periodic crystalline structures. Second, I will describe the Descending from Stochastic Clustering Variance Regression (DiSCoVeR) algorithm to bias the discovery of new suggested materials away from known chemistries in a systematic way towards unintuitive and even unlikely yet promising candidates for new materials.