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DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking

Gabriele Corso, Hannes Stärk, Bowen Jing, Regina Barzilay, Tommi Jaakkola

arXiv:2210.01776v2q-bio.BMcs.LGphysics.bio-ph

TL;DR

Molecular docking requires predicting ligand binding structures, but regression-based deep-learning methods have reduced runtime without substantial accuracy gains. DiffDock instead uses diffusion generative modeling over translational, rotational, and torsional pose degrees of freedom. It achieves 38% top-1 success at RMSD<2 ˚A on PDBBind, outperforms prior search-based and deep-learning methods, and retains higher accuracy on computationally folded structures.

  • Problem

    Regression-based docking methods are faster than traditional search but have not substantially improved accuracy for predicting ligand binding structures.

  • Method

    DiffDock is a diffusion generative model that maps the ligand-pose manifold to translational, rotational, and torsional degrees of freedom.

  • Results

    38% of PDBBind top-1 predictions achieve RMSD<2 ˚A, versus 23% for search-based and 20% for deep-learning methods; DiffDock also achieves 22% on ESMFold-generated structures without further training.

  • Takeaways & Limitations

    DiffDock combines fast inference with confidence estimates and retains substantially higher docking precision on computationally folded protein structures than previous methods.

  • Takeaways & Limitations

    The pose-transformation formulation treats the torsional component as a product space rather than strictly as a group.

Abstract

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Predicting the binding structure of a small molecule ligand to a protein -- a task known as molecular docking -- is critical to drug design. Recent deep learning methods that treat docking as a regression problem have decreased runtime compared to traditional search-based methods but have yet to offer substantial improvements in accuracy. We instead frame molecular docking as a generative modeling problem and develop DiffDock, a diffusion generative model over the non-Euclidean manifold of ligand poses. To do so, we map this manifold to the product space of the degrees of freedom (translational, rotational, and torsional) involved in docking and develop an efficient diffusion process on this space. Empirically, DiffDock obtains a 38% top-1 success rate (RMSD<2A) on PDBBind, significantly outperforming the previous state-of-the-art of traditional docking (23%) and deep learning (20%) methods. Moreover, while previous methods are not able to dock on computationally folded structures (maximum accuracy 10.4%), DiffDock maintains significantly higher precision (21.7%). Finally, DiffDock has fast inference times and provides confidence estimates with high selective accuracy.

1 INTRODUCTION

DiffDock reframes molecular docking as generative modeling and develops diffusion over ligand-pose degrees of freedom. It achieves higher reported accuracy than prior methods, including on computationally folded structures, while supporting confidence-based selection.

  • Traditional docking is slow and inaccurate because it searches a vast, rugged scoring-function landscape.
  • DiffDock models docking as a generative distribution over ligand poses rather than a regression problem.
  • The method diffuses over ligand translation, rotation, and torsion degrees of freedom, then reverses this process to progressively refine random poses.
  • A confidence model ranks sampled poses to provide a final prediction and confidence score while retaining comparison among multiple poses.
  • 22% of top-1 predictions achieve RMSD<2 ˚A on ESMFold-generated structures without further training.
  • 38% of PDBBind blind-docking top-1 predictions achieve RMSD<2 ˚A, versus 23% for search-based and 20% for deep learning methods.

2 BACKGROUND AND RELATED WORK

The background contrasts search-based docking with faster regression-based machine-learning methods and explains why existing diffusion models are not directly suited to docking's restricted pose space.

  • Molecular docking: Molecular docking is divided into known-pocket and blind docking, with this work focusing on blind docking without prior binding-pocket knowledge.
  • Search-based docking methods: Search-based methods combine physics-based scoring functions with stochastic pose searches intended to find a global optimum.
  • Machine learning for blind docking: EquiBind and TANKBind use one-shot or few-shot regression-based predictions that are orders of magnitude faster but have not matched traditional methods' performance.
  • Diffusion generative models: Existing diffusion models learn over the full Euclidean space R3n, whereas docking poses occupy a much more restricted space of degrees of freedom.

3 DOCKING AS GENERATIVE MODELING

The paper argues that regression is mismatched to docking under pose uncertainty and motivates generative modeling, confidence ranking, and likelihood-aligned training objectives.

  • Existing machine-learning methods improve runtime by avoiding search but have not reached search-based docking performance.
  • Docking predictions are useful when their structural deviation does not significantly affect downstream analyses of binding interactions.
  • Maximizing the proportion of predictions within RMSD tolerance is nondifferentiable, motivating likelihood-based generative training.
  • DiffDock samples poses from a diffusion posterior and ranks them with a confidence model for users who need few predictions and an associated confidence measure.
  • Regression tends toward means of uncertain pose alternatives, while generative models aim to capture multiple significant modes.

4 METHOD

DIFFDOCK formulates ligand docking on the lower-dimensional pose manifold induced by rigid-body motion and torsional flexibility, then maps it to a product space where diffusion can be efficiently defined and sampled. The model operates on 3D ligand poses and ranks sampled candidates with a confidence model.

  • Ligand pose transformations: Ligand poses are modeled on an (m + 6)-dimensional manifold defined by six rototranslation degrees of freedom and m rotatable-bond torsions.The model conditions the pose distribution on a protein structure and a seed ligand conformation.
  • Diffusion on the product space: A bijection between the product space and the reachable pose manifold permits diffusion modeling on the product space while retaining correspondence with ligand poses.The product-space construction avoids directly diffusing on the original submanifold.
  • Ligand pose transformations: The pose manifold is represented through ligand translations, rigid rotations, and torsion-angle changes applied to a seed conformation.These transformations define the product space P = T(3) × SO(3) × SO(2)^m and the reachable pose space Mc.
  • Ligand pose transformations: Torsion updates are chosen to minimize RMSD perturbation and remain disentangled from global rotations and translations.The construction ensures zero infinitesimal linear and angular momentum.
  • Diffusion on the product space: The forward diffusion proceeds independently across translation, rotation, and torsion components, with scores and kernels computed separately in each manifold.Translation uses a Gaussian kernel, rotation uses IGSO(3), and torsions use a wrapped normal distribution on the torus.
  • Diffusion model and confidence ranking: Training and inference operate directly on 3D ligand structures, enabling SE(3)-equivariant physical reasoning and reducing dependence on arbitrary torsion-angle definitions.The trained diffusion model generates candidate poses that are then scored by a confidence model trained on whether RMSD is below 2 Å.

5 EXPERIMENTS

Experiments evaluate DIFFDOCK on blind docking and computationally generated apo-structures, finding strong accuracy, speed, and confidence-based selection performance.

  • Docking accuracy: 38.2% top-1 success with 40 sampled poses surpasses GLIDE, TANKBind, and the best pocket-prediction-plus-search baseline.The RMSD <2 Å success rates are 21.8% for GLIDE, 20.4% for TANKBind, and 28.8% for EquiBind+GNINA.
  • Inference runtime: On GPU, DIFFDOCK is 3 to 12 times faster than the best search-based method, GNINA.It remains slower than one-shot EQUIBIND but can be accelerated without significant accuracy loss.
  • Selective accuracy of confidence score: Selective accuracy rises from 38% to 83% when predictions are limited to the one-third of complexes with highest model confidence.Confidence correlates 0.68 with negative RMSD, indicating useful ranking of sampled poses and complexes.

6 CONCLUSION

The paper presents DIFFDOCK as a diffusion-based generative approach to molecular docking that outperforms prior methods, runs quickly, and retains accuracy on computationally folded structures.

  • 6 CONCLUSION: DIFFDOCK applies diffusion generative modeling to ligand docking through a process over the manifold of ligand-pose degrees of freedom.The method uses ligand pose transformations spanning the relevant manifold.
  • 6 CONCLUSION: DIFFDOCK outperforms the state of the art on PDBBind while providing fast inference and confidence estimates with high selective accuracy.The conclusion also reports retained accuracy on computationally folded protein structures.
  • 6 CONCLUSION: The framework is positioned for real-world pipelines and future integration with downstream tasks such as affinity prediction.The paper also identifies protein-protein and protein-nucleic acid docking as possible extensions.

A PROOFS

The proofs establish properties of RMSD alignment and the pose-transformation map used in DIFFDOCK’s geometric construction.

  • Proof of Proposition 1: RMSD alignment removes infinitesimal rotational and translational components, yielding zero linear and angular momentum at t=0.The proof derives this by minimizing the instantaneous velocity norm with respect to translation and angular velocity.
  • Proof of Proposition 1: This disentangling result applies to the infinitesimal action of any arbitrary function, not only the specific transformation form used in the proof.The argument relies on the RMSD alignment property rather than the particular form of B(t, θ, x).
  • Proof of Proposition 2: For a fixed seed conformation, the map from the product space of pose transformations to the accessible conformational manifold is bijective.Surjectivity follows from the manifold’s definition, while injectivity is shown by recovering translation, torsion angles, and rotation under a nondegeneracy assumption.
  • Proof of Proposition 2: The injectivity proof assumes practical conformers are not collinear, allowing equal transformed conformers to imply equal rotations.Under this assumption, equality of conformers forces equality of translation, torsion angles, and rotation parameters.

B TRAINING AND INFERENCE

DiffDock trains a score-based diffusion model over docking degrees of freedom and samples ligand poses by reversing noise on a pose manifold. Training aligns RDKit-generated conformers with ground-truth poses, while inference iteratively updates sampled poses; the group-action formulation is approximate for torsions.

  • B TRAINING AND INFERENCE: Training replaces each ground-truth pose with its closest RDKit-conformer pose to reduce the train–inference manifold shift.The replacement minimizes RMSD within the manifold induced by the RDKit conformer.
  • B TRAINING AND INFERENCE: DiffDock models ligand translation, rotation, and torsion as diffusion variables and reverses noise to generate poses.The diffusion process is defined on a product space representing docking degrees of freedom.
  • B TRAINING AND INFERENCE: The score-based procedure trains on diffusion-kernel perturbations and performs inference through a geodesic random walk driven by predicted scores.The model repeatedly interconverts between the product space and 3D ligand-pose space using a seed conformation.
  • B TRAINING AND INFERENCE: Applying diffusion updates directly to ligand poses is justified by treating the transformation operations as an approximate group action.The approximation becomes increasingly accurate as torsion-angle updates decrease.
  • B TRAINING AND INFERENCE: The approximate group-action procedure works well empirically, but making torsion updates exact remains future work.The authors use the approximate procedure for all reported training and experiments.

C ARCHITECTURE DETAILS

DiffDock represents proteins and ligands as sparse heterogeneous geometric graphs and uses equivariant tensor-product convolutions to predict diffusion scores and pose confidence. Its outputs separately encode translation, rotation, torsion, and a confidence scalar.

  • C ARCHITECTURE DETAILS: Equivariant tensor-product convolutions combine node features with spherical-harmonic edge representations and update features through typed messages.The architecture uses SO(3) irreducible representations implemented with e3nn.
  • C ARCHITECTURE DETAILS: DiffDock’s heterogeneous graph contains ligand atoms, receptor residues, and receptor heavy atoms for confidence modeling.Sparsity supports runtime and memory constraints while providing an inductive bias.
  • C ARCHITECTURE DETAILS: Graph connectivity uses distance cutoffs, neighbor limits, ligand covalent-bond edges, and diffusion-dependent residue–ligand edges.The residue–ligand cutoff expands with translational diffusion noise to preserve likely future interactions.
  • C ARCHITECTURE DETAILS: The score model outputs translational and rotational vectors plus one torsional scalar per rotatable bond.These outputs lie in the tangent spaces associated with translation, SO(3) rotation, and SO(2)^m torsion.
  • C ARCHITECTURE DETAILS: The confidence model aggregates ligand-atom scalar representations into a single SE(3)-invariant confidence score.The aggregated features are passed through a three-layer MLP with batch normalization.

D.1 EXPERIMENTAL SETUP

The experiments use a time-split PDBBind benchmark and evaluate symmetry-corrected ligand RMSD, while also constructing an ESMFold apo-structure benchmark. The setup emphasizes docking against imperfect or nonmatching protein structures as a more realistic test.

  • D.1 EXPERIMENTAL SETUP: The PDBBind time split contains 17k complexes from 2018 or earlier for training and validation, plus 363 non-overlapping 2019 test structures.The split follows prior work and avoids ligand overlap between training and test complexes.
  • D.1 EXPERIMENTAL SETUP: Evaluation reports the percentage of predictions with symmetry-corrected heavy-atom RMSD below 2 Å after aligning protein structures.The 2 Å threshold is treated as a successful pose criterion based on prior work.
  • D.1 EXPERIMENTAL SETUP: PDBBind evaluates docking to corresponding receptor holo-structures, which is simpler and less realistic than docking to apo structures or differently bound holo-structures.The authors therefore examine structures generated by ESMFold.
  • D.1 EXPERIMENTAL SETUP: The ESMFold benchmark aligns receptor residues with exponentially distance-weighted Kabsch fitting, emphasizing residues near ligand atoms.The alignment uses a separately selected smoothing parameter for each complex.
  • D.1 EXPERIMENTAL SETUP: The resulting ESMFold protein structures and associated ligand positions are used to evaluate docking methods on approximate apo-structures.Twelve of 361 ESMFold predictions were discarded after running out of GPU memory.

D.3 IMPLEMENTATION DETAILS: HYPERPARAMETERS, TRAINING, AND RUNTIME MEASUREMENT

The implementation trains separate score and confidence models, measures inference runtimes under stated preprocessing exclusions, and compares DiffDock with established docking baselines. The paper also identifies access to holo-structures as a central scope limitation.

  • D.3 IMPLEMENTATION DETAILS: HYPERPARAMETERS, TRAINING, AND RUNTIME MEASUREMENT: DiffDock’s score model uses exponential moving-average weights, batch size 16, and 20 denoising steps during inference.The final model is selected using validation performance on RMSD below 2 Å.
  • D.3 IMPLEMENTATION DETAILS: HYPERPARAMETERS, TRAINING, AND RUNTIME MEASUREMENT: Hyperparameters are selected with smaller score models before scaling to a 20.24-million-parameter model trained on four 48GB GPUs.The confidence model has 4.77 million parameters and is trained on 28 generated poses per example.
  • D.3 IMPLEMENTATION DETAILS: HYPERPARAMETERS, TRAINING, AND RUNTIME MEASUREMENT: Reported runtimes exclude preprocessing for all methods, including protein embeddings, conformer generation, and radius-graph construction for DiffDock.The reported DiffDock runtime focuses on reverse-diffusion inference.
  • D.3 IMPLEMENTATION DETAILS: HYPERPARAMETERS, TRAINING, AND RUNTIME MEASUREMENT: Baseline comparisons include search-based tools, learned docking models, and hybrid pipelines using default settings unless otherwise specified.The authors note that search exhaustiveness can alter runtime–performance tradeoffs.
  • D.3 IMPLEMENTATION DETAILS: HYPERPARAMETERS, TRAINING, AND RUNTIME MEASUREMENT: DiffDock assumes access to the protein’s bound holo-structure, and fully modeling apo docking requires protein-flexibility modeling left for future work.The method may work when binding-induced conformational changes are largely confined to side chains.

F.1 PHYSICALLY PLAUSIBLE PREDICTIONS

DIFFDOCK’s generative formulation avoids several physically implausible predictions associated with regression-based docking, including self-intersections, steric clashes, and averaged poses between multiple binding modes.

  • DIFFDOCK samples multiple correct binding modes instead of predicting an unphysical mean structure for symmetric complexes.Regression-based methods predict the mean of possible modes, whereas DIFFDOCK can sample around multiple modes.
  • Regression-based methods can produce squashed-up ligand conformations when uncertainty exists about the correct conformer.Square-error minimization places atoms close to the mean conformation.
  • Steric clashes are quantified as heavy-atom distances below 0.4 ˚A between ligand and receptor atoms.This cutoff follows protein-quality assessment tools and previous literature.
  • DIFFDOCK avoids the self-intersections observed in regression-based predictions across the investigated results.The paper reports never finding a self-intersection in DIFFDOCK’s investigated results.
  • DIFFDOCK produces realistic local structures, whereas EquiBind and TANKBind can generate unrealistic geometries such as non-planar aromatic rings.DIFFDOCK’s local structures match realistic RDKit structures.
  • Randomly selected test examples show that DIFFDOCK and GNINA can sometimes nearly perfectly predict the bound structure, while TANKBind often produces self-intersections.

F.2 FURTHER RESULTS AND METRICS

Further evaluations examine robustness across splits, molecular properties, protein-structure quality, and docking metrics. DIFFDOCK’s performance is largely insensitive to training-ligand similarity and remains comparatively strong on approximate ESMFold structures.

  • The evaluation reports RMSD distributions and proportions below 2 ˚A and 5 ˚A for both top-1 and top-5 predictions.
  • DIFFDOCK’s RMSD has negligible Spearman correlation with Tanimoto similarity to the closest training ligand.The reported Spearman rank correlation coefficient is -0.031.
  • DIFFDOCK and GNINA show similar correlations between RMSD and ligand size or rotatable-bond count.
  • DIFFDOCK retains a large part of its accuracy when docking to approximately correct ESMFold backbones, unlike baselines that are highly sensitive to small structural variations.The ESMFold-quality analysis compares docking on crystal and generated structures across groups of pocket-residue RMSD.
  • The reported comparisons include top-1, top-5, apo-structure, and unseen-receptor docking results.These are presented in Tables 5–8 and Figures 6–7.
  • Unseen-receptor evaluation isolates test complexes whose UniProt IDs are absent from DIFFDOCK’s training and validation data.

F.3 ABLATION STUDIES

The ablations identify model size, protein embeddings, reverse-diffusion steps, and sample count as runtime–accuracy controls. Fewer diffusion steps can preserve most performance, while more samples improve confidence-based selection.

  • Model size: Model scaling improved DIFFDOCK performance, with the final score model using 20.24 million parameters.A smaller 3.97-million-parameter model can be trained on a single 48GB GPU.
  • Protein embeddings: ESM2 protein embeddings provide some improvement but are not necessary for state-of-the-art performance.
  • Diffusion steps: DIFFDOCK reaches nearly full performance with 10 reverse-diffusion steps, suggesting a potential 2x speedup with a small accuracy drop.Runtime scales approximately linearly with the number of sequential diffusion steps.
  • Diffusion samples: DIFFDOCK’s runtime scales sublinearly with larger sample counts until samples fit in parallel, after which additional GPU parallelization is straightforward.
  • Diffusion samples: Top-1 success rises from 22% with one diffusion sample to 38% when confidence selection chooses among 40 samples.The confidence model receives independent samples from the diffusion model.
  • Diffusion steps: The reverse-diffusion process is illustrated over 20 steps, showing the highest-confidence sample, other samples, and the crystal structure.
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