Control-Guided Molecular Diffusion for Training-Free Conditional 3D Molecule Generation

Training-free diffusion guidance has attracted increasing attention in conditional 3D molecule generation for its flexibility across new design objectives. However, existing methods largely rely on gradients, while many important molecular constraints are non-differentiable. To handle these, prior works typically approximate gradients using zeroth-order estimation or differentiable surrogates, introducing errors during diffusion and consequently limiting their effectiveness. In this paper, we tackle this challenge from a new perspective. We propose Control-Guided Molecular Diffusion (CGMD), a framework that reformulates training-free molecular guidance as a stochastic optimal control problem and derives an expression for the guidance term that requires only forward evaluations from non-differentiable evaluators, fundamentally bypassing the additional errors brought by gradient recovery. Beyond non-differentiable evaluators, we find that CGMD's control formulation also naturally accommodates differentiable constraints, and further design a hierarchy-preserving control mechanism to handle different constraints. Experiments in non-differentiable and mixed-guidance settings demonstrate the efficacy of our framework.