Molecular structure generation is a fundamental problem that involves determining the 3D positions of molecules’ constituents. It has crucial biological applications, such as molecular docking, protein folding, and molecular design. Recent advances in generative modeling, such as diffusion models and flow matching, have made great progress on these tasks by modeling molecular conformations as a distribution. In this work, we focus on flow matching and adopt an energy-based perspective to improve training and inference of structure generation models. Our view results in a mapping function, represented by a deep network, that is directly learned to iteratively map random configurations, i.e. samples from the source distribution, to target structures, i.e. points in the data manifold. This yields a conceptually simple and empirically effective flow matching setup that is theoretically justified and has interesting connections to fundamental properties such as idempotency and stability, as well as the empirically useful techniques such as structure refinement in AlphaFold. Experiments on protein docking as well as protein backbone generation consistently demonstrate the method’s effectiveness, where it outperforms recent baselines of task-associated flow matching and diffusion models, using a similar computational budget.

Autonomous multi-agent systems are raising in popularity in recent years. More specifically, Unmanned Aerial Vehicles (UAVs) are involved in modern solutions for surveillance, delivering and film shooting. To carry out these tasks, the avoidance of any possible collision is a crucial matter, mostly when agents need to cooperate. In this paper, different collision avoidance algorithms are compared and analyzed for distributed multi-agent holonomic systems. Our purpose is to identify and clarify the different classes of reciprocal collision avoidance algorithms and then to compare them using meaningful metrics and test for the evaluation.