Curriculum Learning for Generative Flexible Docking

Wenyin Zhou; Hossein Azizpour

cs.LGOct 20, 2026

Curriculum Learning for Generative Flexible Docking

Authors: Wenyin Zhou, Hossein Azizpour

Organizations: KTH Royal Institute of Technology · Science for Life Laboratory

Abstract

Flexible docking is a highly practical task, aiming to predict the joint configuration of a protein-ligand complex from a protein apo structure and a ligand SMILES string. Diffusion and flow-based generative models have made this task tractable by modeling the posterior distribution over the ligand pose and the protein conformation conditioned on the apo input. The central challenge, however, remains the long-tailed apo-to-holo structure shift, where a small fraction of protein undergo large conformational changes. In this work, motivated by the practical observation that downweighting large shift examples improves generalization, and by the mixed nature of the long tail consisting of genuinely difficult examples and noisy ones, we propose to use curriculum learning for this task, gradually incorporating large conformational change examples during training. With a linear pacing function, we show that an existing method can be strongly enhanced. On the PDBBind ESMFold apo benchmark, with relaxation and confidence-based pose selection, the resulting model GCLDock achieves a 46.52% top-1 success rate (ligand RMSD less than 2A) and 40.26% when additionally requiring PoseBusters validity, outperforming existing baselines.

Figures & tables

Figure 1: Structure shift of pocket-aligned all-atom RMSD (log scale) between apo and holo conformations on the PDBBind v2020 training set.

Figure 2: Max C-alpha RMSD and competence $\lambda(t)$ of curriculum learning at each epoch.

Method	Ligand RMSD $<2$ Å		AA RMSD $<1$ Å
	Top-10	Average	Top-10	Average
FM Baseline	52.66 $\pm$ 0.32	37.57 $\pm$ 0.60	47.80 $\pm$ 0.71	41.58 $\pm$ 0.51
Geometric	51.82 $\pm$ 0.88	36.98 $\pm$ 0.29	46.41 $\pm$ 0.52	41.68 $\pm$ 0.42
Linear	56.14 $\pm$ 0.84	40.78 $\pm$ 0.43	47.00 $\pm$ 0.26	42.12 $\pm$ 0.25
Root ( $p=2$ )	54.60 $\pm$ 0.69	37.13 $\pm$ 0.82	47.57 $\pm$ 0.50	41.44 $\pm$ 0.51

Table 1: Top-10 and average PDBBind ESMFold docking benchmark. Results are averaged over 5 sampling seeds.

Method	Ligand RMSD		All-Atom RMSD	% PB valid	L-RMSD $<2$ Å and % PB Valid	Runtime (s)
	% $<2$ Å ( $\uparrow$ )	Median (Å) ( $\downarrow$ )	% $<1$ Å ( $\uparrow$ )	( $\uparrow$ )	( $\uparrow$ )
SMINA (rigid)	6.6	7.7	N.A.	–	–	258
SMINA	3.6	7.3	5.2	–	–	1914
GNINA (rigid)	6.7	7.1	N.A.	93.3	6.7	260
GNINA	8.4	7.9	4.5	91.3	7.7	1575
DiffDock-Pocket (rigid)	37.5	3.0	N.A.	25.9	4.9	17

Table 2: Top-1 PDBBind ESMFold docking benchmark. Results are averaged over 5 sampling seeds.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

	Pocket-Alignd Apo-Holo Shift $<2$ Å			Pocket-Alignd Apo-Holo Shift $\geq 2$ Å
Method	Top-10 ligand $<2$ Å	Avg. ligand $<2$ Å	Avg. AA RMSD $<1$ Å	Top-10 ligand $<2$ Å	Avg. ligand $<2$ Å	Avg. AA RMSD $<1$ Å
FM Baseline	58.8 $\pm$ 1.2	43.7 $\pm$ 0.7	58.7 $\pm$ 0.2	40.1 $\pm$ 1.8	24.6 $\pm$ 0.6	6.2 $\pm$ 0.3
Geometric	56.2 $\pm$ 1.7	42.6 $\pm$ 0.4	58.4 $\pm$ 0.4	42.8 $\pm$ 1.7	25.3 $\pm$ 0.7	7.4 $\pm$ 0.3
Linear	62.1 $\pm$ 1.2	47.7 $\pm$ 0.5	59.0 $\pm$ 0.2	44.2 $\pm$ 0.7	27.0 $\pm$ 1.2	7.6 $\pm$ 0.3
Root ( $p=2$ )	60.2 $\pm$ 0.3	44.0 $\pm$ 0.8	58.2 $\pm$ 0.5	43.3 $\pm$ 2.3	23.2 $\pm$ 1.1	6.9 $\pm$ 0.3

Appendix

Table 3: PDBBind test results stratified by the pocket-aligned apo-holo all-atom RMSD. The results are averaged over five sampling seeds.

	Epochs	Complexes	Rel.	RMSD $<2$ Å	Median RMSD
		processed	compute	(%)	(Å)
FM baseline	750	12,240,000	$1.000\times$	52.7	1.87
Geometric	800	10,322,160	$0.843\times$	51.8	1.92
Root ( $p=2$ )	800	11,179,152	$0.913\times$	54.6	1.81
Linear	800	10,769,712	$0.880\times$	56.1	1.77

Appendix

Table 4: Training compute and docking accuracy for the pacing comparison. Accuracy is on the

363

complex PDBBind timesplit test set, averaged over five sampling seeds. Every curriculum run consumes less compute than the baseline despite training for more epochs.

Group	Hyperparameter	Value
Architecture	Total parameters	$72$ M
	Scalar / vector channels ( $n_{s}$ , $n_{v}$ )	$50$ / $10$
	Convolution layers	$6$
	Spherical harmonics degree	$2$
	Max irrep order	$2$ (second-order reps)
	Sigma / distance / cross-distance embed	$64$ / $64$ / $64$

Appendix

Table 5: Training configuration of the curriculum (linear pacing) docking model. The score network is an SE(3)-equivariant tensor-product message passing network operating on a ligand graph, protein residues graph, protein all-atom graph, protein-ligand graph with flexible backbone and side chains. Ligand translations, rotations and torsions each carry an independent noise schedule; protein backbone and sidechain degrees of freedom use fixed noise levels.

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Molecular docking requires reasoning jointly about ligand pose and protein flexibility. Most diffusion-based docking models predict torsional updates with generic Euclidean heads that ignore the periodic geometry of angular variables. This mismatch is especially limiting in flexible docking, where ligand conformations and pocket side chains co-adapt to form the bound complex. Here, we introduce Harmony, a harmonic torsional diffusion framework for flexible protein-ligand docking. Harmony parameterizes ligand and side-chain torsional score fields as derivatives of learned harmonic potentials on the circle, which are noised mode by mode in the Fourier basis owing to the properties of variance-exploding diffusion on the torus. This construction makes periodicity explicit and gives the model a frequency-aware inductive bias over rotameric motion. On the PDBBind benchmark, Harmony improves ligand pose accuracy and pocket all-atom reconstruction over recent flexible docking methods. On PoseBusters, it improves the physical validity of generated complexes. Case studies on EBNA1 and KRAS G12D illustrate the method's behavior on a polar and a shallow binding site, respectively. Together, these results indicate that aligning the score parameterization with the geometry of the diffusion process is a simple and effective lever for improving flexible docking.

Abstract

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