[Paper Review] AdsorbFlow: energy-conditioned flow matching enables fast and realistic adsorbate placement

Jiangjie Qiu, Wentao Li+3 more|arXiv (Cornell University)|Feb 22, 2026

Machine Learning in Materials Science0 citations

TL;DR

AdsorbFlow uses energy-conditioned deterministic flow matching to place adsorbates on surfaces, achieving state-of-the-art DFT-verified adsorption minima with only 5 generative steps, greatly outperforming diffusion and brute-force baselines. It generalizes to out-of-distribution systems and supports different equivariant backbones.

ABSTRACT

Identifying low-energy adsorption geometries on catalytic surfaces is a practical bottleneck for computational heterogeneous catalysis: the difficulty lies not only in the cost of density functional theory (DFT) but in proposing initial placements that relax into the correct energy basins. Conditional denoising diffusion has improved success rates, yet requires $\sim$100 iterative steps per sample. Here we introduce AdsorbFlow, a deterministic generative model that learns an energy-conditioned vector field on the rigid-body configuration space of adsorbate translation and rotation via conditional flow matching. Energy information enters through classifier-free guidance conditioning -- not energy-gradient guidance -- and sampling reduces to integrating an ODE in as few as 5 steps. On OC20-Dense with full DFT single-point verification, AdsorbFlow with an EquiformerV2 backbone achieves 61.4% SR@10 and 34.1% SR@1 -- surpassing AdsorbDiff (31.8% SR@1, 41.0% SR@10) at every evaluation level and AdsorbML (47.7% SR@10) -- while using 20 times fewer generative steps and achieving the lowest anomaly rate among generative methods (6.8%). On 50 out-of-distribution systems, AdsorbFlow retains 58.0% SR@10 with a MLFF-to-DFT gap of only 4~percentage points. These results establish that deterministic transport is both faster and more accurate than stochastic denoising for adsorbate placement.

Motivation & Objective

• Address the bottleneck of locating low-energy adsorption geometries in computational catalysis.
• Develop a deterministic, energy-conditioned transport model to replace stochastic diffusion for adsorbate placement.
• Leverage classifier-free guidance to condition on relative energies without requiring energy-gradient guidance.
• Demonstrate backbone-agnostic design with principled rotation heads for SE(3) equivariant networks.
• Evaluate on OC20-Dense with DFT verification and assess out-of-distribution generalization.

Proposed method

• Model the adsorbate–slab system as a rigid body with in-plane translation t and SO(3) rotation R on a 2-torus and SO(3).
• Learn a time-dependent vector field v_theta(x, t | c) on the configuration manifold via conditional flow matching with rectified-flow trajectories.
• Incorporate energy conditioning E_rel through classifier-free guidance, randomly dropping the energy condition during training and combining conditional/unconditional predictions at inference with guidance weight w.
• Train with pairs (x0, x1) where x0 is a relaxed minimum and x1 is a perturbed placement, using geodesic interpolation for rotation and linear interpolation for translation.
• Perform sampling by integrating an ODE backward in time for K steps (default 5), starting from random noise, then relax generated placements with MLFF and verify with DFT.

Figure 1: AdsorbFlow overview. Training: A linear interpolant connects the relaxed pose $x_{0}$ (at $t{=}0$ ) to noise $x_{1}$ (at $t{=}1$ ), and a symmetry-aware E(3)-equivariant network predicts the velocity field. Sampling: Starting from initial noise $x_{1}$ at $t{=}1$ , we integrate the ODE bac

Experimental results

Research questions

• RQ1 Can energy-conditioned deterministic transport outperform stochastic diffusion for adsorbate placement in OC20-Dense?
• RQ2 How does backbone expressivity (EquiformerV2 vs PaiNN) interact with CFG guidance in shaping sampling and accuracy?
• RQ3 What is the impact of using 5 generative steps on DFT-verified success, anomaly rates, and OOD generalization compared to prior methods?
• RQ4 To what extent can MLFF-based pre-screening reliably rank candidates for subsequent DFT verification across ID and OOD data?
• RQ5 How do rotation-head designs affect SE(3) equivariance and placement quality across backbones?

Key findings

• AdsorbFlow with EquiformerV2 backbone achieves 34.1% SR@1 and 61.4% SR@10 on OC20-Dense with 5 steps, surpassing AdsorbDiff and AdsorbML at every level.
• With 5 steps, AdsorbFlow is a 20× reduction in backbone evaluations compared to diffusion baselines while maintaining higher accuracy.
• On ID, MLFF-to-DFT gaps are 11.3 pp for EqV2 and 15.9 pp for PaiNN at SR@10; on OOD these gaps shrink to 4.0 pp and 2.0 pp respectively.
• AdsorbFlow maintains 58.0% SR@10 on a 50-system OOD split, with a MLFF-to-DFT gap of 4.0 pp for EqV2 and 2.0 pp for PaiNN, indicating strong generalization.
• Anomaly rates at k=10 are 6.8% for EqV2 and 13.6% for PaiNN on ID, demonstrating diverse and plausible placements across seeds.