Boltzmann-Expected Molecular Design with Decoupled Annealing Flows
Selma Moqvist, Richard Beckmann, Ross Irwin, Rocío Mercado, Simon Olsson
stat.ML, cs.LG
Submitted: 2026-07-21
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
Terminology
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.
Sources
- Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation
- FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation
- FlexiFlow: decomposable flow matching for generation of flexible molecular ensemble
- Implicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular Dynamics
- Multi-state Protein Design with DynamicMPNN
- Structure-based Drug Design with Equivariant Diffusion Models
- Exploring Discrete Flow Matching for 3D De Novo Molecule Generation
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