AdsorbFlow: energy-conditioned flow matching enables fast and realistic adsorbate placement

A central challenge in computational catalysis is the identification of low-energy and chemically plausible adsorption configurations, as these directly affect adsorption energies, reaction pathways, and catalytic performance. Existing approaches generally rely on enumerating candidate adsorption sites followed by iterative refinement through density functional theory calculations or machine-learning-based relaxations. However, such workflows remain computationally expensive and are difficult to scale to complex surfaces or multi-adsorbate systems. Here, we introduce Meta-LegNet, a graph learning framework that combines SE(3)-equivariant atom-level message passing with voxel-based multiscale aggregation and cross-domain meta-learning to learn transferable representations of local adsorption environments across diverse catalyst--adsorbate systems. Rather than following a conventional regression-only paradigm, Meta-LegNet encodes local chemical environments using invariant radial features and equivariant directional information, and further incorporates broader structural context through coordinate-frame voxel pooling, assignment-based upsampling, and gated feature fusion. The resulting local-global decomposition produces atom-resolved attribution maps, which are processed to identify adsorption-relevant local environments in an interpretable manner. Based on the learned representations, we further construct an adsorption-environment database and develop a template-matching strategy to propose likely adsorption sites on previously unexplored surfaces without exhaustive site enumeration. Overall, our results suggest that learning transferable adsorption environments provides an accurate, interpretable, and practical route for accelerating catalyst screening.

Flow Matching has emerged as a leading framework for generative modeling, powering state-of-the-art systems such as FLUX and Stable Diffusion 3.5. However, the iterative nature of its ODE-based sampling process creates a fundamental efficiency bottleneck: the quality of generated samples is highly sensitive to the choice of step-sizes, and current models typically require 20 to 30 steps for good quality. In this work, we propose two lightweight, training-free algorithms, CAT-OV and CAT-OT that adapt step-sizes at inference time based on a novel connection between Flow Matching sampling and gradient flow. Our algorithms are computed efficiently by not requiring additional neural function evaluations. Specifically, CAT-OT estimates curvature over time via a finite-difference approximation of the time-derivative of the vector field, while CAT-OV approximates curvature over the state space via a gradient of the vector field. Under suitable conditions, both methods have truncation error bounds of constant order. Empirically, CAT-OV and CAT-OT outperform existing step-size heuristics in image quality metrics across four text- to-image Flow Matching models, reducing the number of generation steps required to reach comparable quality by up to 40%.

Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a primary challenge is to learn an efficient sampler. We introduce Flow Sampling, a framework built on diffusion models and flow matching for the data-free setting. Our training objective is conditioned on a noise sample and regresses onto a denoising diffusion drift constructed from the energy function. In contrast, diffusion models' objective is conditioned on a data sample and regresses onto a noising diffusion drift. We utilize the interpolant process to minimize the number of energy function evaluations during training, resulting in an efficient and scalable method for sampling unnormalized densities. Furthermore, our formulation naturally extends to Riemannian manifolds, enabling diffusion-based sampling in geometries beyond Euclidean space. We derive a closed-form formula for the conditional drift on constant curvature manifolds, including hyperspheres and hyperbolic spaces. We evaluate Flow Sampling on synthetic energy benchmarks, small peptides, large-scale amortized molecular conformer generation, and distributions supported on the sphere, demonstrating strong empirical performance.