EVA-Flow: Learning Shared Chemistry for Unified Environment-Aware Molecular Conformation Generation

1 Introduction

• Molecular geometry changes across solvent, crystal-lattice, and protein-pocket environments, although the underlying chemistry remains unchanged.Source: §1 · pp. 1–2
• Existing generative models commonly target vacuum or one context, using separate models for different settings.Source: §1 · p. 1
• The framework formulates conformer generation as learning shared chemistry under environment-specific constraints rather than training isolated models for each environment.Source: §1 · p. 2
• EVA-Flow combines an environment encoder, learned harmonic base, variational latent, and flow-matching architecture to support low-data cross-environment transfer.Source: §1 · p. 2
• Pretraining and cross-environment finetuning improve accuracy most clearly in data-scarce environments, with same-molecule and multi-reference evidence of environmental responsiveness.UMA relaxation separately supports physical validity for generated Vacuum conformers.Source: §1 · p. 2

2 Related Work

• Flow matching regresses a velocity field that transports a base distribution to data, while related variants extend it to conditional generation and 3D molecular settings.Source: §2 · p. 2
• Hybrid VAE–flow models either apply flow matching in latent space or use flow matching as a decoder; EVA-Flow adopts the decoder form.Source: §2 · p. 2
• Most molecular conformer-generation methods target a single setting, typically vacuum or protein–ligand docking, and require separate models per setting.Source: §2 · p. 2
• Unlike latent-space molecular diffusion, EVA-Flow performs flow matching in data space and explicitly conditions on the environment.Source: §2 · p. 2

3.1 Problem Formulation

• The target graph G describes the molecule being generated, while the environment graph GE supplies conditioning context whose construction varies by environment.The target graph retains the same semantics across settings; at inference, the model uses G, GE, and their listed attributes.Source: §3.1 · p. 3, Table 1 · p. 4

3.2 Model Architecture

• A three-layer GCN and two-layer MLP map GE to an embedding e that conditions both the molecular encoder and decoder.The encoder processes G, target coordinates x, and e to produce node-level variational posterior parameters.Source: §3.2 · p. 4
• The encoder’s latent pathway captures residual molecule–environment variability during training, but the reported checkpoint has a collapsed latent posterior.The paper reports that the coupled base and latent nevertheless aid low-data cross-environment transfer.Source: §3.2 · p. 4
• A conditional Harmonic base and stochastic flow-matching decoder transport samples toward conformations conditioned on G and e.At inference, sampling starts from a graph-only Harmonic prior and integrates the learned flow field from t = 0 to t = 1.Source: §3.2 · pp. 4–5

3.3 Training Objectives

• Four jointly optimized losses regulate train–inference transitions: latent-prior and base regularization, latent consistency, and flow matching.The KL and consistency terms constrain information pathways that could act as training-time shortcuts, while the flow-matching term retains information needed for accurate generation.Source: §3.3 · pp. 6–7

4.1 Datasets

• The five-dataset pretraining corpus contains 445,662 molecule entries and 9.8M conformations, followed by finetuning in four environments.The benchmarks use GEOM-DRUGS for Vacuum, PDBBind-v2020 for Docking, Aquamarine for Solvation, and COD for Packing.Source: §4.1 · p. 7

4.2 Experimental Setup

• Four training strategies compare individual or unified finetuning, each with or without pretraining, while the default protocol generates four conformers per test molecule.Vacuum and Solvation also support multi-conformer evaluation; Docking and Packing provide one physical reference each.Source: §4.2 · pp. 8–9

4.3 Results

• Accuracy gains are concentrated in data-scarce Docking, Solvation, and Packing; unified setups substantially surpass Individual finetuning in these settings.Pretraining also provides gains over Individual training in data-scarce environments; the paper reports EVA-Flow outperforms ETKDG+MMFF in all four environments and GFN2-xTB on Solvation.Source: §4.3 · p. 9

4.4 Analysis

• Across all six environment pairs, generated conformations are closer on average to their own environment’s reference than to the other environment’s reference.The gap is largest for Solvation–Vacuum and smallest for Packing–Docking; Packing–Docking’s similar references and generations are consistent with context-responsive rather than label-forced differences.Source: §4.4 · pp. 9–10

4.5 Ablation Studies

• The FM decoder, Harmonic base, and SE(3)-equivariance are essential across environments, while the learned base and VAE latent provide consistent gains in tested transfer regimes.Removing both learned base and latent lowers Recall COV in all twelve transfer comparisons, with the largest gap in low-data Solvation, up to −0.255 Recall COV.Source: §4.5 · p. 13

5 Conclusion

• Pretraining and unified finetuning yield their largest gains in the three data-scarce environments, while multi-reference Solvation and shared-molecule analyses support ensemble coverage and environment-responsive generation.The framework conditions a shared flow-matching backbone on representations of vacuum, protein pockets, solvation descriptors, and crystal metadata.Source: §5 · p. 13
• More expressive backbones, scaling, multi-reference benchmarks, and environment-specific physical validation could extend accuracy and evaluation beyond current settings.Unseen environments such as surface adsorption and solid–liquid interfaces remain future work.Source: §5 · p. 13

Broader Impact Statement

• Generated structures should be checked with physical calculations and domain expertise before downstream use, especially in safety-critical applications.The method is not intended to replace experimental validation or high-accuracy physical simulation.Source: Broader Impact Statement · p. 13

A Data Preparation

• Pretraining combines QM9 and DRUGS, SPICE and CREST-relaxed SPICE, and vacuum-relaxed crystal-forming molecules from OE62.The SPICE relaxation pipeline excludes molecules with cis/trans stereo-SMILES because stereochemistry is not preserved.Source: A Data Preparation · pp. 16–17
• AQM provides implicit-water conformers and four solvation descriptors; its default protocol selects the dataset’s c1 (index-0) conformer rather than ranking by energy.The split contains 1,276 training, 175 validation, and 157 test molecules.Source: A Data Preparation · p. 17
• COD preparation filters for validated, non-disordered organic crystals with Z′ = 1, while PDBBind examples pair ligand structures with protein-pocket environment graphs.COD topology is recovered by maximum-common-substructure matching; PDBBind retains 9,940 training, 614 validation, and 218 test examples.Source: A Data Preparation · p. 17

B Distributions of Atom Counts and Rotatable-Bond Counts

• Pretraining-set molecules average roughly 17–44 atoms and typically have fewer than 15 rotatable bonds; finetuning sets average roughly 38–64 atoms, with a long PDBBind tail.The histograms describe molecular size and flexibility across the listed datasets.Source: B Distributions of Atom Counts and… · pp. 17–18, Figure 6 · p. 18, Figure 7 · p. 19

C Training Details and Hyperparameters

• Pretraining and unified finetuning each run for 800 epochs; unified finetuning allocates nominal samples across Vacuum, Packing, Docking, and Solvation, while individual finetuning uses each environment’s full training set.The unified epoch yields 91,216 effective samples after allocations are capped by dataset size.Source: C Training Details and Hyperparameters · p. 19

Training and checkpointing

• AdamW training uses gradient clipping, linear warmup, and cosine decay; the lowest-validation-loss checkpoint supplies reported results.The schedule peaks at 5 × 10^-4 and decays to 10^-8; validation is performed every epoch.Source: §C.1 · p. 19, Table 6 · p. 20

Reproducibility

• Table 2 reports mean ± standard deviation across five inference-sampling seeds from a fixed checkpoint, not training uncertainty.Training uses seed 42; the separate all-conformer ETFlow diagnostic uses six runs.Source: §C.1 · p. 20

Inference

• The default SDE sampler uses 50 integration steps, while deterministic ODE sampling trades a small amount of Vacuum Recall COV for speed.Vacuum Recall COV is 0.737 for ODE versus 0.747 for SDE; the inference perturbation schedule is distinct from the training interpolation.Source: §C.1 · p. 20

Inference time and compute

• EVA-Flow is modestly faster than retrained ETFlow per molecule at the same step count in this implementation; each 800-epoch pretraining or unified-finetuning stage takes about 67 wall-clock hours.The timing uses a single A100 GPU for inference and eight A100 GPUs for training.Source: §C.1 · p. 20, Table 7 · p. 21

D Evaluation Metric Definition

• AMR and Recall and Precision COV assess geometric matches between generated and reference conformers, with lower AMR indicating closer matches.Recall COV measures reference coverage; Precision COV measures the fraction of generated samples close to the finite reference set.Source: D Evaluation Metric Definition · p. 21
• Recall and Precision should be read jointly: Recall grows with sample budget, while Precision penalizes generated samples that do not match the finite reference set.The RMSD threshold δ differs by environment: 0.5 Å for Solvation, 0.75 Å for Vacuum and Packing, and 2.0 Å for Docking.Source: D Evaluation Metric Definition · p. 21

E.1 Additional Precision Results

• Precision Coverage plots cover all four environments; under the four-conformer, one-reference protocol, median Coverage is quantized and often identical across models.Mean COV and median AMR provide finer discrimination in Table 2.Source: §E.1 · p. 21, §E.2 · p. 21, Figure 8 · p. 22

E.3 Generation Diversity

• Pairwise heavy-atom best-RMS measurements show non-zero spread among generated conformers in every environment, indicating non-trivial sample diversity.The measure averages unique pairs among four generated conformers per molecule.Source: §E.3 · p. 22

E.5 Physical Reference Methods

• RDKit ETKDG with MMFF relaxation and GFN2-xTB with ALPB-water solvation serve as physical reference methods, not controlled environment-conditioning ablations.GFN2-xTB is included for Solvation; the table captions describe the evaluation scope.Source: §E.5 · p. 23, Table 11 · p. 24

E.4 Multi-Reference Solvation Evaluation

• 0.981 Recall shows that the single-conformer-trained model covers the available Solvation ensemble under the multi-reference protocol.Aquamarine test molecules average 37 conformers, with up to 431 references.Source: §E.4 · pp. 22–23, Table 10 · p. 24

E.6 Reconciling Published and Retrained ETFlow Results

• On Vacuum under the 2K protocol, EVA-Flow is comparable to retrained ETFlow, exceeds MCF-L on Precision COV, but trails it on Recall COV.EVA-Flow versus ETFlow: Recall COV 0.721 vs. 0.712 and Precision COV 0.707 vs. 0.704; EVA-Flow versus MCF-L: Recall COV 0.721 vs. 0.847 and Precision COV 0.707 vs. 0.668.Source: §E.6 · p. 24
• Only comparisons within matched evaluation blocks support model comparisons; cross-dataset or cross-pipeline values are diagnostic because preprocessing, references, and sampling budgets differ.The published ETFlow benchmark uses all available references and a 2K budget, unlike the cleaned default benchmark.Source: §E.6 · p. 24, Table 12 · p. 25

F Physical Validity of Generated Conformers

• UMA relaxation finds very small energy changes and atomic displacements for 4,000 generated Vacuum conformers, indicating proximity to local UMA energy minima.Coverage and AMR alone measure geometric similarity, not energetic plausibility.Source: F Physical Validity of Generated… · p. 24, Table 13 · p. 25

G Shared-Molecule Controls

• After shared molecules are excluded from finetuning, the own-versus-cross pattern persists for pairs with well-separated references; Packing–Docking remains weakly separated.This supports a conditioning effect on held-out molecules rather than finetuning memorization; broad pretraining still includes Vacuum molecules.Source: Table 14 · p. 25, G Shared-Molecule Controls · p. 25

H Environment-Graph Sensitivity

• Zeroing solvation descriptors, lattice parameters, or the docking environment embedding degrades performance, with the docking pocket most critical.These are inference-time feature ablations without retraining.Source: Table 15 · p. 26, H Environment-Graph Sensitivity · p. 26

• Replacing the flow-matching decoder with regression collapses Recall COV by targeting the conditional mean of a multi-modal distribution.Source: I Full Ablation Metrics · p. 26
• Table 16 provides complete metrics for original ablations across all four environments; NoBase reduces performance within the original base–latent parameterization, while latent-free training has mixed Individual-training effects and trails the full model in all twelve cross-environment transfer comparisons.Source: I Full Ablation Metrics · p. 26
• The NoBase variant reduces performance within the original base–latent parameterization.Source: I Full Ablation Metrics · p. 26

• In all twelve cross-environment transfer comparisons, the full model outperforms the latent-free variant, with gaps concentrated in low-data Solvation.The reported Solvation Recall COV gaps are −0.16 to −0.26.Source: J Latent-Free Model: Full… · p. 26, Table 18 · p. 27
• Under Individual training, latent-free Recall COV changes from 0.728 to 0.727 in Vacuum, 0.553 to 0.470 in Docking, 0.414 to 0.503 in Solvation, and 0.512 to 0.493 in Packing.Source: J Latent-Free Model: Full… · p. 26, Table 18 · p. 27
• The latent-free model removes both the learned base and VAE latent while retaining the environment embedding, fixed harmonic base, and flow-matching decoder.Source: J Latent-Free Model: Full… · p. 26, Table 18 · p. 27

K Data Exposure and Balanced Sampling

• Solvation Recall COV drops 10.7% under balanced sampling despite unchanged Solvation molecules per epoch, while Unified outperforms Individual on DRUGS despite seeing 48.0M versus 218.1M samples.Small-data Individual models’ validation loss plateaus by approximately epochs 30–50, so extra repetitions alone do not explain the gains.Source: K Data Exposure and Balanced Sampling · p. 28

L Train–Test Consistency of the Base Distribution

• The inference-time prior closely matches the learned base, and the large NoBase drop is attributed to an optimization interaction rather than inference-time mismatch.At convergence, measured divergence is 0.036 nats on validation and 0.026 on training; measured eigenvalue modes are within 1% of unity.Source: L Train–Test Consistency of the Base… · p. 28, Table 20 · p. 29, Table 21 · p. 29

M Latent Posterior-Collapse Diagnostics

• In the Pretrain+Unified checkpoint, the latent posterior is effectively collapsed; setting z to zero leaves metrics effectively unchanged, so performance is not attributed to information carried by z.The decoder primarily conditions on molecular graph G and environment e.Source: M Latent Posterior-Collapse Diagnostics · p. 29, Table 22 · p. 29

N Loss-Weight Sensitivity

• In 21 of 24 cells, one-at-a-time regularizer changes of 0.1× or 10× shift Recall COV by less than 0.045; Solvation is sensitive to particular settings.The experiment does not vary network capacity or interactions among weights.Source: N Loss-Weight Sensitivity · pp. 29–30, Table 23 · p. 30

O Environment-Encoder Equivariance

• The SE(3)-equivariant encoder improves Docking accuracy but is neutral or worse in contexts dominated by topology, proxies, or scalar descriptors.In the separate rotation test, the GCN embedding changes 1.33% on average, while the equivariant encoder changes approximately 10−5; this measures embedding stability, not end-to-end coordinate equivariance.Source: O Environment-Encoder Equivariance · p. 30, Table 24 · p. 30

P Aquamarine Conformer-Selection Sensitivity

• Reference sensitivity is tested by changing the test reference or training target while holding the model, split, sampling seed, or training budget controlled within each comparison block.The matched target-rule models use a smaller 200-epoch budget than the 800-epoch model and are compared only within their block.Source: P Aquamarine Conformer-Selection… · p. 30, Table 25 · p. 31, Table 26 · p. 31

Q Molecule Visualization

• Figure 9 compares aligned pairwise heavy-atom RMSDs for shared molecules in Solvation–Docking and Packing–Docking; darker heatmap cells indicate lower RMSD.The panels contain 12 Solvation–Docking and 59 Packing–Docking molecules; Table 27 visualizes shared Packing–Docking conformers aligned to Docking references.Source: Q Molecule Visualization · p. 30, Figure 9 · p. 31, Table 27 · p. 32