EvoEGF-Mol: Evolving Exponential Geodesic Flow for Structure-based Drug Design

TL;DR

EvoEGF-Mol reframes structure-based drug design as sampling along evolving exponential geodesics on the Fisher–Rao information manifold, enabling joint refinement of molecular geometry and discrete chemistry. By replacing static Dirac endpoints with dynamic concentrating targets, it avoids boundary singularities and maintains well-conditioned intermediate distributions, trained via KL transport objectives. The approach achieves competitive to state-of-the-art geometric fidelity and binding-pose metrics on CrossDocked while delivering improved scaffold-quality on MolGenBench, and ablations confirm the necessity of the evolving endpoint and explicit bond diffusion. This framework offers a principled, geometry-aware path for de novo drug design, with practical impact in producing geometrically realistic candidates and guiding future integration of activity data for improved pharmacology.

Abstract

Structure-Based Drug Design (SBDD) aims to discover bioactive ligands. Conventional approaches construct probability paths separately in Euclidean and probabilistic spaces for continuous atomic coordinates and discrete chemical categories, leading to a mismatch with the underlying statistical manifolds. We address this issue from an information-geometric perspective by modeling molecules as composite exponential-family distributions and defining generative flows along exponential geodesics under the Fisher-Rao metric. To avoid the instantaneous trajectory collapse induced by geodesics directly targeting Dirac distributions, we propose Evolving Exponential Geodesic Flow for SBDD (EvoEGF-Mol), which replaces static Dirac targets with dynamically concentrating distributions, ensuring stable training via a progressive-parameter-refinement architecture. Our model approaches a reference-level PoseBusters passing rate (93.4%) on CrossDock, demonstrating remarkable geometric precision and interaction fidelity, while outperforming baselines on real-world MolGenBench tasks by recovering bioactive scaffolds and generating candidates that meet established MedChem filters.

Figures (11)

• Figure 1: The EvoEGF-Mol concept. EvoEGF-Mol generates molecules by exponential geodesics on a statistical manifold. To address the singularity at the manifold boundary, we use a Dynamic Endpoint strategy. By defining a time-evolving target (solid curve), the model creates a stable path that gradually concentrates from the prior to the data, guiding the sampling process from noise to valid molecular structures.
• Figure 2: Comparison of (a) Exponential Geodesic Flow and (b) Evolving Exponential Geodesic Flow. Both paths transition from a one-dimensional standard Gaussian distribution toward a target Dirac distribution at $x=2$. (Left) Evolution of PDFs over time. (Middle) Trajectories of natural parameters over time. (Right) Trajectories of standard parameters over time. The evolving path prevents the premature variance collapse seen in the standard geodesic, ensuring smoother transition dynamics for molecular generation.
• Figure 3: The training and sampling process of EvoEGF-Mol. EvoEGF-Mol trains a neural network to map noisy intermediate states to terminal parameters by minimizing KL divergence along evolving exponential geodesics. During inference, molecular structures are generated through iterative refinement, with look-ahead predictions guiding state transport from prior to data distribution. See Appendix \ref{['sec:app-train_sample_algo']} for details.
• Figure 4: Bond length and bond angle distributions for the most common bond types in the CrossDock test set. Results for additional bond types are provided in Appendix \ref{['sec:more_eval_res']}. Our EvoEGF-Mol consistently exhibits improved accuracy in reproducing molecular geometries.
• Figure 5: Ablation study on Dirichlet parameter settings, the Dirichlet smooth vector, smooth coefficients, bond generation, and the effectiveness of EvoEGF, in terms of binding affinity, strain energy, and PB-Valid.