Generating Physically Consistent Molecules with Energy-Based Models

Generating chemically valid 3D molecular conformations is critical for computational drug discovery. Classical diffusion-based models like GeoLDM perform well but require hundreds of steps, making large-scale in silico screening impractical. Recent efforts on few-step molecular generation have accelerated this process to 12-50 steps, but they often largely sacrifice sample stability. In this work, we present FlashMol, an ultra-fast molecule generative model producing high-quality molecular conformations in as few as 4 steps. To achieve this, we adapt distribution matching distillation (DMD) - a reverse KL-divergence minimization objective - to the molecular domain for effective distillation. Considering the local minimization behavior of DMD, we respace the molecule generation timesteps, providing the generator with much better initialization and enables effective distillation. Additionally, to mitigate the mode-seeking behavior of DMD and improve diversity, we further regularize it with a Jensen-Shannon divergence term, which incorporates the mean-seeking behavior of the forward KL divergence. Extensive experiments on QM9 and GEOM-DRUG datasets demonstrate that FlashMol matches and even surpasses the original 1000-step teacher, achieving up to 250$\times$ acceleration in sampling speed while maintaining high molecular quality.

Generating stable molecular conformations typically forces a tradeoff between the physical realism of energy-based relaxation and the sampling efficiency of data-driven generative models. While machine learning force fields (MLFFs) can sample stable conformations by relaxing molecular geometries according to physical forces, they require costly ab-initio training data. Conversely, diffusion models (DMs) learn from equilibrium data alone but are dependent on noise schedules and time-step conditioning. In this work, we propose generative pseudo-force fields (GPFFs) to bridge these paradigms by training an MLFF on a quadratic pseudo-potential energy surface relative to reference equilibrium structures. Because no ab-initio calculations are required for the perturbed geometries, non-equilibrium training data can be generated on the fly by perturbing the equilibria with Gaussian noise. We show that GPFFs constitute a time-step-agnostic variant of variance exploding DMs: the score comes from the predicted pseudo-forces but because force magnitudes implicitly encode the noise level, no time-step conditioning is needed. Our GPFF can hence be used as a drop-in replacement in standard diffusion sampling (ancestral, Heun) but also facilitates more efficient, adaptive variants and an MLFF inspired direct denoising scheme. Our proposed sampling algorithms support arbitrary structural priors and geometric constraints. On QM9, GPFF has 100 % validity at 256 neural function evaluations (NFE) and over 50 % at just 6 NFE, outperforming diffusion baselines across all samplers. Combined with custom priors, we showcase the fast and accurate generation process of our method in a molecular editor for a drug design setting, where a molecule is generated in real time.

Most 3D properties relevant to molecular design, including free energies and shape descriptors, are $\textit{expectations}$ 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 $\textbf{Boltzmann-expected design}$ and realise it with $\textbf{DECAF}$ (Decoupled Annealing Flows), which factorise the joint distribution over graphs and coordinates into two conditional flow models: a graph-conditioned flow $p(x\mid\mathcal{G})$, acting as a $\textit{Boltzmann emulator}$, and a coordinate-conditioned flow $p(\mathcal{G}\mid x)$, 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 $p(x\mid\mathcal{G})$, 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 $\textbf{higher-moment design}$: 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.