The usefulness of molecules generated with VR enumeration hinges on the quality of the underlying reaction rules. In particular, for the simpler molecules required in particular in hit expansion and hit to lead scenarios, virtual screening on such libraries can work well and is now routinely used in academia and industry: VR-enumerated libraries compiled by vendors such as Enamine have been very successfully used in prospective VS campaigns, leading to an ≈80% success rate in synthesis More recently, generative models for molecules have been suggested as construction algorithms. These refer to a variety of machine learning models, for example autoregressive models, (variational) autoencoders, normalizing flows or diffusion models, which can be trained on target chemical spaces, and then sample new molecules from that space as if one would sample from probability distribution over molecules. Generative models for molecules can be trained on different representations, for example SMILES, molecular graphs, fragment graphs, or 3D molecular structures, and also perform de novo design, for example when coupled with fine-tuning or RL algorithms. Despite their simplicity, SMILESbased autoregressive models (also called Chemical Language Models, CLMs), have shown robust performance to generate reasonable and synthesizable molecules when trained on previously synthesized, drug-like molecules, and have been experimentally validated (see below). However, in particular when used in de novo design, generative models based on atomistic representations can be pushed towards generating unreasonable or hard to synthesize molecules, even though to a lesser degree than previous, unconstrained de novo design algorithms, if the exploration is not carefully restricted. A promising newer direction are generative models for forward synthesis routes, which similar to the VR approach generate molecules and synthesis routes, leading to much more reasonable structures ]: Bradshaw et al. proposed generative models that construct multi-step forward reaction routes where the model learns to pick building blocks and intermediates, which are then submitted to a reaction predictor . They demonstrated competitive performance of their algorithm on the Guacamol benchmark compared to less restricted generative models, while maintaining synthesizability. By switching the reaction model to reaction rules, and changes to the tree generation process, Gao et al. recently reported a generative model for reaction routes that does not use a reaction predictor, but can learn to choose which reactions to run. They demonstrated competitive performance to strong baselines on the TDC generative benchmark, while maintaining synthesizability and molecule quality. They also demonstrated that their model could generate synthesizable analogs using conditional molecule generation, as well as forward synthesis planning. However, this approach has not been scaled up yet to more complex rule-bases, thus limiting the size the chemical space the model can explore. Gottipatti et al. proposed a reinforcement rearning-based approach to generate routes in the forward direction, however, their algorithm is limited to generating linear reaction routes, instead of more general tree-shaped routes . Recently, also hybrid algorithms combining atom-based generative models with reaction-driven generation emerged. Despite this progress, and proven uses for simpler, early stage molecules, current reaction-driven construction algorithms, both enumeration-based and generative models, still have a number of limitations: The predicted routes depend on the quality of single step reaction models or reaction rule-base. Current reaction models, for example the Molecular Transformer, will always predict a product, or even hallucinate completely incorrect structures, even when a reaction is not going to proceed. On the other end, compiling and maintaining high quality rule-bases is time-consuming, and does not scale . The breadth and complexity of chemistry captured by these models is still limited, leading to a restricted exploration of chemical space. Improvements could be made by incorporating models that can be trained on positive and negative reactions, such as the in-scope filter models introduced by Segler and Coley , even though significantly more effort needs to be made to gather the required training data. It is also an open question to what extent reaction-driven generation, which is discrete, limits the exploration of chemical space, making optimization during de novo design harder than compared to models which can more flexibly exchange atoms in a molecule.