DiSCO: Diffusion Schrödinger Bridge for Molecular Conformer Optimization

The generation of energetically optimal 3D molecular conformers is crucial in cheminformatics and drug discovery. While deep generative models have been utilized for direct generation in Euclidean space, this approach encounters challenges, including the complexity of navigating a vast search space. Recent generative models that implement simplifications to circumvent these challenges have achieved state-of-the-art results, but this simplified approach unavoidably creates a gap between the generated conformers and the ground-truth conformational landscape. To bridge this gap, we introduce DiSCO: Diffusion Schrödinger Bridge for Molecular Conformer Optimization, a novel diffusion framework that enables direct learning of nonlinear diffusion processes in prior-constrained Euclidean space for the optimization of 3D molecular conformers. Through the incorporation of an SE(3)-equivariant Schrödinger bridge, we establish the roto-translational equivariance of the generated conformers. Our framework is model-agnostic and offers an easily implementable solution for the post hoc optimization of conformers produced by any generation method. Through comprehensive evaluations and analyses, we establish the strengths of our framework, substantiating the application of the Schrödinger bridge for molecular conformer optimization. First, our approach consistently outperforms four baseline approaches, producing conformers with higher diversity and improved quality. Then, we show that the intermediate conformers generated during our diffusion process exhibit valid and chemically meaningful characteristics. We also demonstrate the robustness of our method when starting from conformers of diverse quality, including those unseen during training. Lastly, we show that the precise generation of low-energy conformers via our framework helps in enhancing the downstream prediction of molecular properties. The code is available at https://github.com/Danyeong-Lee/DiSCO.