Elign: Equivariant Diffusion Model Alignment from Foundational Machine Learned Force Fields

Abstract

Generative models for 3D molecular conformations must respect Euclidean symmetries and concentrate probability mass on thermodynamically favorable, mechanically stable structures. However, E(3)-equivariant diffusion models often reproduce biases from semi-empirical training data rather than capturing the equilibrium distribution of a high-fidelity Hamiltonian. While physics-based guidance can correct this, it faces two computational bottlenecks: expensive quantum-chemical evaluations (e.g., DFT) and the need to repeat such queries at every sampling step. We present Elign, a post-training framework that amortizes both costs. First, we replace expensive DFT evaluations with a faster, pretrained foundational machine-learning force field (MLFF) that estimates molecular energies and forces. Second, we eliminate repeated run-time queries by shifting physical steering to the post-training phase. To achieve the second amortization, we formulate reverse diffusion as a reinforcement learning problem and propose to use Group Relative Policy Optimization (GRPO) to fine-tune the denoising policy. Our objective combines a potential-based energy reward and a force-based stability reward, which are optimized in a disentangled fashion. Experiments show that Elign generates conformations with lower gold-standard DFT energies and forces, while improving stability. Crucially, inference remains as fast as unguided sampling, since no energy evaluations are required during generation.