Boltzmann-Expected Molecular Design with Decoupled Annealing Flows
Authors: Selma Moqvist, Richard Beckmann, Ross Irwin, Rocío Mercado, Simon Olsson
Abstract
Most 3D properties relevant to molecular design, including free energies and shape descriptors, are expectations over the Boltzmann distribution over 3D configurations of a molecular graph. However, existing property-guided generative models tie each property to a single structure, ignoring the underlying ensemble. We recast 3D molecular design as Boltzmann-expected design and realise it with DECAF (Decoupled Annealing Flows), which factorise the joint distribution over graphs and coordinates into two conditional flow models: a graph-conditioned flow p(x∣G), acting as a Boltzmann emulator, and a coordinate-conditioned flow p(G∣x), proposing new graphs from 3D information. By alternating the two flows, DECAF optimises molecular graphs with a simulated-annealing acceptance rule whose scoring function is evaluated on ensembles drawn from p(x∣G), making ensemble statistics, not single-conformer properties, the design target. The resulting loop requires no retraining to change objectives. On GEOM-Drugs, we show that ensemble-aware optimisation produces graphs whose mean radius of gyration and solvent-accessible surface area consistently shift toward targets, while single-conformer optimisation degrades on larger drug-like molecules where Boltzmann distributions are broadest. DECAF extends to multi-objective trade-offs and, uniquely among 3D generative models, to higher-moment design: jointly optimising an ensemble property's variance and skewness to produce flexible molecules biased to a prescribed conformational regime: we verify the conformational distributions of these higher-moment designs with all-atom MD simulations.
Molecular design is typically approached as a problem of finding molecules which can adopt a single bioactive conformation. In reality, molecules occupy a distribution over conformations, and many of the properties which determine whether a candidate is viable depend on that distribution rather than on any single conformer. We reframe molecular design as an optimisation of both the modes and properties of molecules' conformational ensembles, where modes can be represented as shapes, pharmacophore profiles or protein pockets, and properties are aggregate scalars computed over the whole distribution. To realise this we introduce ensemble-conditioned guidance, a framework which conditions 3D molecular generative models on both axes simultaneously. Mode conditions are composed adaptively at inference by combining the vector fields produced under each condition. Conditions may be targeted or avoided, mixed across modalities and combined in arbitrary numbers, allowing a wide range of design tasks to be expressed with a single trained model. We introduce adaptive symmetry learning to allow conditions from different reference frames to be composed, and extend our generative framework to enable flexible-size generation. We evaluate on new benchmarks for multi-mode conditioning and ensemble property optimisation, and apply the framework to two practical drug discovery tasks, dual-target binder design and active-state-selective agonist design, where in both cases conditioning on the additional state improves the desired outcome over single-state conditioning.
The success of generative molecular design hinges on a model's steerability toward high-reward samples. Because many molecular properties are intrinsically linked to molecular size, accurately capturing the joint distribution of properties and the number of atoms is essential. However, current diffusion and flow-based models fix the number of atoms, which ultimately limits their ability to navigate this complex relationship. To address this, we introduce Morph, a flexible-size generative model for conditional and unconditional 3D molecular design based on geometric graphs. By dynamically adapting size, Morph can seamlessly integrate existing structural priors, like scaffolds, and significantly enhances property steering. We show that Morph matches current fixed-size state-of-the-art models while offering the benefit of unparalleled sampling flexibility. We demonstrate out-of-distribution generation in regimes where previous models fail, paving the way for enhanced generative modeling for molecular design.
Molecules in equilibrium follow a Boltzmann distribution, making the underlying energy landscape a physically grounded modeling objective. However, such landscapes are difficult to learn from data and, once learned, hard to sample from. Diffusion and flow-matching models sidestep these difficulties by learning a time-conditional score or transport field between noise and data, losing the energy inductive bias in exchange for a more tractable training objective. We introduce EBMol, an energy-based model (EBM) that restores this inductive bias by learning an atom-additive scalar potential without explicit simulation during training. Our method employs a flow-inspired Restoring Field Matching objective to approximate the energy landscape. We adopt the Mirror-Langevin algorithm for sampling, enabling unified updates of atomic positions and types, and incorporate parallel tempering for inference-time compute scaling. EBMol is the first EBM for 3D molecular generation to achieve state-of-the-art performance on QM9 and GEOM-Drugs. Moreover, we show that the learned energy landscape serves as a principled quality metric for ranking and filtering configurations, and demonstrate controllable generation without retraining through shape-steered sampling via potential composition and zero-shot linker design.
Christoph Griesbacher, Lea Bogensperger, Andreas Habring +1