MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space

Yanru QuKeyue QiuYuxuan SongJingjing GongJiawei HanMingyue ZhengHao ZhouWei-Ying Ma

article2024ICML56 citations

Proposes MolCRAFT, a structure-based drug design model operating in continuous parameter space with noise-reduced sampling to generate structurally realistic 3D molecular conformations while achieving reference-level binding affinities without mode collapse.

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Structure-based drug design uses three-dimensional biological target structures to generate therapeutic molecule candidates computationally. While modern generative methods propose high-affinity binders, they frequently generate physically unrealistic structures—a problem known as false positives. Sequential autoregressive models suffer from mode collapse by repeatedly producing narrow sets of simple rings, while diffusion models struggle with the mathematical gap between continuous atomic positions and discrete atom types, leading to high-strain, distorted geometries and severe steric clashes.

The article demonstrates that shifting the generative process into a unified, continuous parameter space resolves these conformational and structural issues. The primary objective is to evaluate a new model, MolCRAFT, which integrates Bayesian Flow Networks with three-dimensional symmetry preservation and a noise-reduced sampling strategy, against leading autoregressive and diffusion frameworks on standard benchmark targets.

The approach was evaluated on the CrossDocked benchmark dataset using 100,000 training protein-ligand pairs and 100 test proteins, sampling 100 molecules per test target under controlled molecule sizes. MolCRAFT models both continuous atomic coordinates and discrete atom types as continuous probability distributions, updating parameters smoothly during generation and bypassing intermediate discrete sampling noise.

The key findings demonstrate major improvements across binding quality, physical stability, and computational speed. First, MolCRAFT achieved a reference-level binding score of -6.59 kcal/mol on generated 3D poses without requiring artificial optimization, outperforming competing baselines by up to -0.84 kcal/mol. Second, it lowered median molecular strain energy to 195 kcal/mol—reducing physical distortion by roughly an order of magnitude compared to diffusion baselines, which exhibited median strain energies between 421 and 1,243 kcal/mol. Third, 41.8% of its generated complexes remained within 2 Å of docking positions upon verification, outperforming all baselines and closely matching natural binding consistency. Finally, MolCRAFT generated complete and valid molecules with a 96.7% success rate in 141 seconds per 100 samples, representing an approximate 24-fold to 44-fold acceleration over leading diffusion models.

These results show that earlier artificial high affinity scores were largely distorted artifacts of redocking software rearranging poorly formed poses. By capturing realistic interatomic interactions directly in three dimensions, MolCRAFT provides a more dependable virtual drug screening pipeline. This reduces the risk of wasting expensive laboratory synthesis resources on structurally unfeasible computational false positives, while drastically cutting computational runtimes.

Organizations developing computational discovery pipelines should consider transitioning from hybrid continuous-discrete diffusion methods to unified continuous parameter frameworks. Benchmarking protocols must also enforce strict controls on candidate molecular sizes, as unconstrained size inflation creates misleadingly high affinity scores. Before committing candidates to physical synthesis, teams should conduct wet-lab experimental validations to confirm actual binding performance.

Confidence in these computational benchmarks is high given the extensive comparative metrics across 100 test proteins. However, the evaluation relies on in silico docking approximations and simulated datasets, which can introduce distribution shifts. Practical adoption must account for the boundary conditions of computational modeling until validated by wet-lab synthesis.

Shanghai Institute of Materia Medica, Chinese Academy of Sciences Tsinghua University University of Illinois Urbana-Champaign architecture designs control parameters generative model MolCRAFT structure-based drug design continuous parameter space

arXiv: 2404.12141 AlgoMole/MolCRAFT

Paper: Equivariant Diffusion for Molecule Generation in 3D, Emiel Hoogeboom et al. (2022). Introduces equivariant 3D diffusion for joint continuous coordinates and categorical atom types, establishing the foundational 3D generative baseline that MolCRAFT aims to surpass by eliminating discrete sampling noise.
Paper: SE(3) diffusion model with application to protein backbone generation, Jason Yim et al. (2023). Formulates SE(3)-equivariant continuous generative dynamics on 3D biological structures, providing mathematical and algorithmic foundations for MolCRAFT's symmetry-preserving generation.
Paper: Geometric and Physical Quantities improve E(3) Equivariant Message Passing, Johannes Brandstetter et al. (2022). Develops steerable E(3)-equivariant graph neural networks that handle directional physical vectors, directly informing symmetry preservation in 3D molecular generation models.
Paper: Matching Normalizing Flows and Probability Paths on Manifolds, Heli Ben-Hamu et al. (2022). Establishes continuous normalizing flow matching on geometric manifolds, underpining continuous trajectory generation methods used to model 3D molecular conformations.
Paper: Diffusion Models: A Comprehensive Survey of Methods and Applications, Ling Yang et al. (2022). Provides a comprehensive taxonomy and mathematical formulation of diffusion probabilistic frameworks and fast sampling techniques that MolCRAFT benchmarks against.

Paper: Stochastic Interpolants: A Unifying Framework for Flows and Diffusions, Michael S. Albergo et al. (2025). Unifies continuous flows and diffusions through finite-time stochastic interpolants, providing theoretical foundations that extend continuous parameter space generative frameworks like MolCRAFT.
Paper: SE(3)-Stochastic Flow Matching for Protein Backbone Generation, Avishek Joey Bose et al. (2024). Applies continuous stochastic flow matching and Brownian bridge dynamics to 3D biological macro-structures, extending continuous generative principles to full protein backbones.
Paper: FlowMM: Generating Materials with Riemannian Flow Matching, Benjamin Kurt Miller et al. (2024). Generalizes unified continuous flow matching across atomic positions, lattices, and discrete elements to periodic 3D crystal structures.
Paper: Protein Conformation Generation via Force-Guided SE(3) Diffusion Models, Yan Wang et al. (2024). Integrates physical force-field guidance into SE(3) generative modeling to resolve steric clashes and high-energy strain in complex macromolecular conformational generation.
Paper: Context-weighted Discrete Flow Matching, Daniil Cherniavskii et al. (2026). Explores context-weighted modifications to discrete flow matching, offering an alternative generative trajectory strategy for molecular and sequence design.
Paper: Discrete State Diffusion Models: A Sample Complexity Perspective, Aadithya Srikanth et al. (2026). Derives formal sample complexity bounds for discrete-state generative diffusion, offering complementary theoretical perspectives on discrete versus continuous parameter representations.

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Abstract

Generative models for structure-based drug design (SBDD) have shown promising results in recent years. Existing works mainly focus on how to generate molecules with higher binding affinity, ignoring the feasibility prerequisites for generated 3D poses and resulting in false positives. We conduct thorough studies on key factors of ill-conformational problems when applying autoregressive methods and diffusion to SBDD, including mode collapse and hybrid continuous-discrete space. In this paper, we introduce MolCRAFT, the first SBDD model that operates in the continuous parameter space, together with a novel noise reduced sampling strategy. Empirical results show that our model consistently achieves superior performance in binding affinity with more stable 3D structure, demonstrating our ability to accurately model interatomic interactions. To our best knowledge, MolCRAFT is the first to achieve reference-level Vina Scores (-6.59 kcal/mol) with comparable molecular size, outperforming other strong baselines by a wide margin (-0.84 kcal/mol). Code is available at https://github.com/AlgoMole/MolCRAFT.

Topics

architecture designs control parameters generative model optimization prototyping systems design hierarchical model

Keywords

MolCRAFT structure-based drug design continuous parameter space molecule generation target protein binding molecular docking molecular conformation drug-like properties force field optimization continuous atom coordinates

1. Introduction
2. Challenges of Generative Models in SBDD
2.1. Failure Modes of Generated Molecules
2.2. Molecular Mode Collapse
2.3. Hybrid Continuous-Discrete Space
3. Preliminary
3.1. Problem Definition
3.2. Molecular Generation in Parameter Space
4. Methodology
4.1. Resolving Different Modalities in Parameter Space
4.2. Noise Reduced Sampling in Parameter Space
5. Experiments
5.1. Experimental Setup
5.2. Main Results
5.3. Ablation Study of Sampling Strategy
6. Related Work
7. Conclusion
Acknowledgements
Impact Statement
References
A. Detailed Formulation of BFN
B. Proof of SE-(3) Invariant Objective and SE-(3) Equivariant Sampling Process
C. Implementation Details
C.1. Parameterization with SE-(3) Equivariant Network
C.2. Featurization
C.3. Model Hyperparameters
D. Additional Experimental Results
D.1. Full Evaluation Results
D.2. Ablation Studies

Knowls

Knowl 1 — MolCRAFT Unified Parameter Space for Continuous Coordinates and Discrete Atom Types
model/method
MolCRAFT formulates structure-based drug design (SBDD) within a Bayesian Flow Network (BFN) operating entirely in a unified, continuous parameter space $\theta = [\theta^x, \theta^v]$ to eliminate the continuous-discrete discrepancy common in hybrid molecular diffusion models.

Given a protein binding pocket $P = \{(x_P^{(i)}, v_P^{(i)})\}_{i=1}^{N_P}$ with $N_P$ atoms ( $x_P^{(i)} \in \mathbb{R}^3$ , $v_P^{(i)} \in \mathbb{R}^{D_P}$ ), the objective is to generate a ligand molecule $M = \{(x_M^{(i)}, v_M^{(i)})\}_{i=1}^{N_M}$ ( $x_M^{(i)} \in \mathbb{R}^3$ , $v_M^{(i)} \in \mathbb{R}^{D_M}$ ), denoted compactly as $p = [x_P, v_P]$ and $m = [x_M, v_M]$ .
1. Continuous Atom Coordinates $\theta^x$ : Coordinates $x$ are parameterized by a Gaussian distribution $\mathcal{N}(x \mid \mu, \rho^{-1} I)$ with parameter $\theta^x = \{\mu, \rho\}$ , where $\mu \in \mathbb{R}^{N_M \times 3}$ is learned and $\rho \in \mathbb{R}$ is accumulated precision. For coordinate noise factor $\alpha_i$ , the Bayesian update function $\{\mu_i, \rho_i\} \leftarrow h(\{\mu_{i-1}, \rho_{i-1}\}, y^x_i, \alpha_i)$ is: $\rho_i = \rho_{i-1} + \alpha_i$ $\mu_i = \frac{\mu_{i-1}\rho_{i-1} + y^x_i \alpha_i}{\rho_i}$ Continuous coordinate noise defines the sender distribution: $p_S(y^x \mid x_M; \alpha) = \mathcal{N}(y^x \mid x_M, \alpha^{-1} I)$
2. Discrete Atom Types $\theta^v$ : Atom types $v$ are parameterized by categorical probabilities $\theta^v \in \mathbb{R}^{N_M \times K}$ , where $K$ is the number of atom types. For noise parameter $\alpha'_i$ , the Bayesian update is: $h(\theta^v_{i-1}, y^v_i, \alpha'_i)_k = \frac{\exp(y^v_{i,k}) (\theta^v_{i-1})_k}{\sum_{j=1}^K \exp(y^v_{i,j}) (\theta^v_{i-1})_j}$ Continuous Gaussian noise is applied to discrete one-hot representations $e_{v_M} \in \mathbb{R}^{N_M \times K}$ via the sender distribution: $p_S(y^v \mid v_M; \alpha') = \mathcal{N}(y^v \mid \alpha'(K e_{v_M} - 1), \alpha' K I)$
3. Receiver Distributions: The neural network $\Phi(\theta_{i-1}, p, t_i)$ reconstructs the clean molecule estimate $\hat{m} = [\hat{x}, \hat{v}] \sim p_O(m \mid \theta_{i-1}, p; t_i)$ , giving receiver distributions: $p_R(y^x \mid \theta^x, p; t) = \mathcal{N}(y^x \mid \hat{x}(\theta^x, p, t), \alpha^{-1} I)$ $p_R((y^v)^{(d)} \mid \theta^v, p; t) = \sum_{k=1}^K p_O^v(k \mid \theta; t) \, p_S^v((y^v)^{(d)} \mid k; \alpha')$ for each atom $d \in \{1, \dots, N_M\}$ .
Knowl 2 — MolCRAFT Noise-Reduced Sampling in Continuous Parameter Space
algorithm
Standard Bayesian Flow Network sampling draws noisy sample-space latents $y_i$ at each step ( $\{ \theta_{i-1} \xrightarrow{\Phi} \hat{m} \xrightarrow{p_S} y_i \xrightarrow{p_U} \theta_i \}$ ), which reintroduces high variance, especially for discrete atom types. MolCRAFT performs noise-reduced sampling directly in the continuous parameter space by taking the continuous expectation $\hat{m} = [\hat{x}, \hat{v}]$ from the output network $\Phi$ and evaluating the Bayesian flow distribution $p_F(\theta_i \mid \hat{m}, p; t)$ in closed form:

$\gamma(t) = \frac{\beta(t)}{1 - \beta(t)}$ $p_F(\mu \mid \hat{x}, p; t) = \mathcal{N}(\mu \mid \gamma(t)\hat{x}, \gamma(t)(1-\gamma(t))I)$ $p_F(\theta^v \mid \hat{v}, p; t) = \mathbb{E}_{y^v \sim \mathcal{N}(y^v \mid \beta'(t)(K e_{\hat{v}} - 1), \beta'(t)KI)} \left[ \delta(\theta^v - \text{softmax}(y^v)) \right]$
function update(x_hat, v_hat, beta_t, beta_prime_t, t)
    gamma = beta_t / (1.0 - beta_t)
    sample mu ~ N(gamma * x_hat, gamma * (1.0 - gamma) * I)
    sample y_v ~ N(beta_prime_t * (K * e_v_hat - 1.0), beta_prime_t * K * I)
    theta_v = softmax(y_v along atom type dimension)
    return mu, theta_v
end function
Input: Network Phi, pocket features p, sampling steps N, atom count n_M, type count K, hyperparams sigma_1, beta_1
Output: Generated molecule [x_hat, v_hat]
mu = 0
rho = 1
theta_v = matrix of shape (n_M, K) filled with 1.0 / K
for i = 1 to N do
    t = (i - 1) / N
    x_hat, v_hat = Phi(mu, theta_v, p, t)
    beta_t = sigma_1^(-2 * t) - 1.0
    beta_prime_t = (t^2) * beta_1
    mu, theta_v = update(x_hat, v_hat, beta_t, beta_prime_t, t)
end for
x_hat, p_v_O = Phi(mu, theta_v, p, 1.0)
sample v_hat ~ p_v_O
return [x_hat, v_hat]
Sampling runs for $N = 100$ steps with noise schedules $\beta_1 = 1.5$ and $\sigma_1 = 0.03$ .
Knowl 3 — MolCRAFT Discrete-Time Training Objective and Loss Formulation
algorithm
MolCRAFT is trained using an $n$ -step discrete-time variational lower bound objective minimizing the Kullback-Leibler (KL) divergence between the sender distribution $p_S$ and receiver distribution $p_R$ over $n$ discretization steps:

$L^n(m, p) = \mathbb{E}_{i \sim \mathcal{U}(1, n)} \mathbb{E}_{y_i \sim p_S, \theta_{i-1} \sim p_F} \left[ D_{\text{KL}}(p_S \parallel p_R) \right] = L_x^n + L_v^n$
1. Coordinate Loss (analytic Gaussian KL divergence): $L_x^n = D_{\text{KL}}\left(\mathcal{N}(x_M, \alpha_i^{-1} I) \parallel \mathcal{N}(\hat{x}(\theta_{i-1}, p, t), \alpha_i^{-1} I)\right) = \frac{\alpha_i}{2} \|x_M - \hat{x}(\theta_{i-1}, p, t)\|^2 = \frac{1 - \sigma_1^{2/n}}{2 \sigma_1^{2i/n}} \|x_M - \hat{x}\|^2$
2. Atom Type Loss: $L_v^n = \ln p_S(y^v \mid v_M; \alpha) - \sum_{d=1}^{N_M} \ln \left( \sum_{k=1}^K p_O(k \mid \theta; t) \, p_S((y^v)^{(d)} \mid k; \alpha) \right)$
Input: Ligand coordinates x_M, ligand types v_M, pocket p, hyperparams sigma_1, beta_1, training steps n
Output: Scalar loss L_n
i ~ UniformInteger(1, n)
t = (i - 1) / n
beta_t = sigma_1^(-2 * t) - 1.0
beta_prime_t = (t^2) * beta_1
sample mu ~ p_F^x(mu | x_M, p; t, beta_t)
sample theta_v ~ p_F^v(theta_v | v_M, p; t, beta_prime_t)
x_hat, v_hat = p_O(mu, theta_v, p, t)
L_x = ((1.0 - sigma_1^(2.0 / n)) / (2.0 * sigma_1^(2.0 * i / n))) * ||x_M - x_hat||^2
alpha = beta_1 * (2 * i - 1) / (n^2)
sample y_v ~ p_S^v(y_v | v_M, alpha)
L_v = ln p_S^v(y_v | v_M; alpha) - ln p_R^v(y_v | v_hat; alpha, t)
return L_x + L_v
The model is trained with $n = 1000$ training steps, Adam optimizer (learning rate $0.005$ , batch size $8$ ), exponential moving average of parameters with decay factor $0.999$ , converging within 15 epochs.
Knowl 4 — SE(3) Invariance of Likelihood and SE(3) Equivariant Coordinate Sampling
theoretical result
Let $T_g(x) = R x + b$ denote an arbitrary transformation in the Special Euclidean group $\mathrm{SE}(3)$ , where $R \in \mathrm{SO}(3)$ is a 3D rotation matrix and $b \in \mathbb{R}^3$ is a 3D translation vector.

Preconditions:
1. The center of mass (CoM) of the protein atom coordinates is translated to zero: $\tilde{x}_P = Q x_P$ where $Q = I_3 \otimes (I_{N_P} - \frac{1}{N_P} \mathbf{1}_{N_P} \mathbf{1}_{N_P}^\top)$ . Ligand atom coordinates $x_M$ and parameter mean $\mu$ are translated by the identical protein CoM vector, defining zero-CoM representations $\tilde{p}, \tilde{m}, \tilde{\mu}$ .
2. The neural network backbone $\Phi(\mu, x_P)$ is an $\mathrm{SE}(3)$ -equivariant graph neural network satisfying $\Phi(R \mu, R x_P) = R \Phi(\mu, x_P)$ .
Result:
1. The loss objective is $\mathrm{SE}(3)$ -invariant: $\|T_g(x_M) - T_g(\hat{x})\|^2 = \|R x_M + b - R \hat{x} - b\|^2 = \|R(x_M - \hat{x})\|^2 = \|x_M - \hat{x}\|^2$ Consequently, the likelihood is invariant to joint $\mathrm{SE}(3)$ transformations on the protein-ligand complex: $p_\phi(T_g(m \mid p)) = p_\phi(m \mid p)$ .
2. Sampling generation in continuous parameter space produces coordinate outputs $x_N$ that are $\mathrm{SE}(3)$ -equivariant with respect to the pocket coordinates $x_P$ .
Knowl 5 — MolCRAFT SE(3)-Equivariant PosNet3D Backbone and Graph Featurization
model/method
MolCRAFT parameterizes the denoising network $\Phi(\theta, p, t)$ using PosNet3D on dynamically constructed dual graphs: a $k$ -nearest neighbors ( $k=32$ ) graph between ligand and protein atoms, and a fully connected graph between ligand atoms.

For each layer $l \in \{0, \dots, L-1\}$ ( $L=9$ , hidden dimension $128$ , $16$ attention heads, ReLU activations with Layer Normalization): $h_i^{l+1} = h_i^l + \sum_{j \in \mathcal{N}_G(i)} \phi_h(d_{ij}^l, h_i^l, h_j^l, e_{ij}, t)$ $\Delta x_i = \sum_{j \in \mathcal{N}_G(i)} (x_j^l - x_i^l) \, \phi_x(d_{ij}^l, h_i^{l+1}, h_j^{l+1}, e_{ij}, t)$ $x_i^{l+1} = x_i^l + \Delta x_i \cdot \mathbf{1}_{\text{mol}}$ where $\mathcal{N}_G(i)$ is the neighborhood of atom $i$ , $d_{ij}^l = \|x_i^l - x_j^l\|_2$ , $e_{ij}$ is a 4-dimensional one-hot edge type (protein-protein, ligand-ligand, protein-ligand, ligand-protein), and $\mathbf{1}_{\text{mol}}$ restricts coordinate updates to ligand atoms only. $\phi_h$ and $\phi_x$ are multi-head attention blocks using $h_i^l$ as query and $[h_i^l, h_j^l, e_{ij}]$ as keys and values. Distance features are expanded using radial basis functions.

Initializations and Featurization:
- Layer 0 inputs: $x^0 = [\mu, x_P]$ and $h^0 = \text{linear}(\theta^v, v_P, t)$ .
- Protein features $v_P$ : one-hot element (H, C, N, O, S, Se), 20-dim one-hot amino acid type, 1-dim backbone indicator, 1-hot arm/scaffold pocket region indicator.
- Ligand features: 1-hot element (C, N, O, F, P, S, Cl), 1-hot aromatic vs. non-aromatic indicator.
- Output layer: directly yields coordinate estimate $\hat{x} = \Phi^x$ and categorical distributions $\hat{v}^{(d)} = \text{softmax}((\Phi^v)^{(d)})$ .

Knowl 6 — Benchmark Evaluation of MolCRAFT on CrossDocked2020 Dataset

data/table

Evaluation of generated molecules on 100 test protein pockets from CrossDocked2020 (100 samples per pocket) under molecular size control. MolCRAFT achieves reference-level direct Vina Scores (-6.59 kcal/mol vs -6.36 kcal/mol for reference) without requiring redocking-based pose rearrangements, while maintaining the highest Binding Feasibility (33.8%) and lowest median Strain Energy among diffusion baselines (195 kcal/mol vs 1243 kcal/mol for TargetDiff).

Methods	Vina Score ()		Vina Min ()		Vina Dock ()		Strain Energy ()			Clash ()	RMSD ()	SA ()	QED ()	BF ()	Size
	Avg.	Med.	Avg.	Med.	Avg.	Med.	25%	50%	75%	Avg.	% < 2Ä	Avg.	Avg.	(%)	Avg.
Reference	-6.36	-6.46	-6.71	-6.49	-7.45	-7.26	34	107	196	5.51	34.0	0.73	0.48	29.0	22.8
AR	-5.75	-5.64	-6.18	-5.88	-6.75	-6.62	259	595	2286	4.49	31.1	0.64	0.51	17.3	17.7
Pocket2Mol	-5.14	-4.70	-6.42	-5.82	-7.15	-6.79	102	189	374	6.24	30.8	0.76	0.57	24.6	17.7
Ours-small	-5.96	-5.89	-6.33	-6.04	-6.98	-6.63	44	103	274	4.88	38.6	0.74	0.52	33.3	17.8
FLAG	16.48	4.53	1.21	-4.04	-5.63	-6.61	143	396	1164	40.83	8.2	0.70	0.49	3.8	21.5
TargetDiff	-5.47	-6.30	-6.64	-6.83	-7.80	-7.91	369	1243	13871	10.84	29.4	0.58	0.48	14.4	24.2
Decomp-R	-5.19	-5.27	-6.03	-6.00	-7.03	-7.16	115	421	1424	8.16	22.7	0.66	0.51	14.6	21.2
Ours	-6.59	-7.04	-7.27	-7.26	-7.92	-8.01	83	195	510	7.09	41.8	0.69	0.50	33.8	22.7
Decomp-O	-5.67	-6.04	-7.04	-7.09	-8.39	-8.43	379	983	4133	14.63	23.9	0.61	0.45	11.1	29.4
Ours-large	-6.61	-8.14	-8.14	-8.42	-9.25	-9.20	171	333	1110	10.73	42.7	0.62	0.46	31.1	29.4

Definitions: BF (Binding Feasibility) is the percentage of generated molecules simultaneously satisfying Vina Score $< -2.49$ kcal/mol, Strain Energy $< 836$ kcal/mol, and symmetry-corrected ligand-redocking RMSD $< 2\text{\AA}$ (95th percentile reference thresholds). Clash counts steric overlap interactions in the protein-ligand complex.

Knowl 7 — Substructural Bond and Angle Geometry Distribution Fidelity
empirical result
MolCRAFT captures substructural geometric distributions with higher fidelity than existing autoregressive and diffusion-based SBDD models, as measured by the Jensen-Shannon Divergence (JSD) between generated and reference distributions across bond lengths, bond angles, and torsion angles on the CrossDocked test set.
1. Average Substructural JSD Summary:
- Bond Length JSD: MolCRAFT achieves $0.319$ , outperforming Decomp-R ( $0.348$ ), Decomp-O ( $0.359$ ), TargetDiff ( $0.382$ ), Pocket2Mol ( $0.485$ ), and AR ( $0.554$ ).
- Bond Angle JSD: MolCRAFT achieves $0.379$ , outperforming FLAG ( $0.406$ ), Decomp-R ( $0.412$ ), Decomp-O ( $0.414$ ), TargetDiff ( $0.435$ ), and Pocket2Mol ( $0.482$ ).
- Torsion Angle JSD: MolCRAFT achieves $0.322$ , superior to TargetDiff ( $0.410$ ), Pocket2Mol ( $0.464$ ), and AR ( $0.547$ ), trailing only FLAG ( $0.270$ , which is explicitly fragment-based but produces $0.2\%$ unparseable outlier molecules).
1. Multi-Modal Bond Length Distribution Capture: While autoregressive baselines (AR, Pocket2Mol) collapse to unimodal bond lengths across diverse bond types, MolCRAFT is the only tested model that successfully recovers the true multi-modal bond length distributions characteristic of C-C, C-N, and C-O chemical bonds.
Knowl 8 — Mode Collapse in Autoregressive SBDD Models
empirical result
Atom-based autoregressive SBDD models exhibit severe mode collapse, generating repetitive substructures due to unnatural sequential ordering constraints during generation. In contrast, MolCRAFT achieves high uniqueness and balanced ring distributions matching natural reference molecules on the CrossDocked benchmark:
1. Sample Uniqueness (percentage of unique generated molecules per pocket):
- AR: $36.2\%$
- Pocket2Mol: $73.7\%$
- DecompDiff-R: $50.3\%$
- DecompDiff-O: $61.6\%$
- TargetDiff: $99.6\%$
- FLAG: $99.7\%$
- MolCRAFT: $97.7\%$
1. Ring Substructure Proportions (relative to ring-containing molecules):
- Fused Rings: Reference $= 30.0\%$ , Train $= 21.6\%$ . Pocket2Mol collapses heavily toward fused rings ( $52.0\%$ ), whereas MolCRAFT matches the reference closely ( $30.9\%$ ).
- 3-Membered Rings: Reference $= 4.0\%$ , Train $= 3.8\%$ . AR exhibits severe pathological mode preference ( $50.8\%$ 3-membered rings), whereas MolCRAFT produces $0.0\%$ .
- 6-Membered Rings: Reference $= 84.0\%$ , Train $= 90.9\%$ . AR yields $71.9\%$ , Pocket2Mol $88.6\%$ , and MolCRAFT $85.1\%$ .
Knowl 9 — Ablation of Parameter-Space Sampling Strategy and Computational Efficiency
empirical result
Ablation experiments comparing parameter-space sampling against data-space sampling across step counts on 100 test proteins (10 samples per pocket) demonstrate significant gains in both binding quality and sampling speed:
1. Binding Affinity Boost: Switching from data-space sampling to parameter-space noise-reduced sampling improves the mean Vina Score / Vina Min from $-5.42$ / $-6.30$ kcal/mol to $-6.51$ / $-7.13$ kcal/mol.
2. Sampling Step Convergence: Unlike data-space sampling (which requires 1000 steps and degrades due to over-smoothing at fine noise scales), parameter-space sampling reaches optimal molecular property scores (QED, Synthetic Accessibility, Completeness) within $100$ sampling steps.
3. Runtime and Generation Success: MolCRAFT generates 100 samples in $141$ seconds with $96.7\%$ Generation Success (valid and complete molecules). This represents a $24.3\times$ speedup over TargetDiff ( $3428$ seconds for 100 samples) and a $43.9\times$ speedup over DecompDiff ( $6189$ seconds for 100 samples).

Knowl 10 — Protein-Ligand Interaction Counts Under Molecular Size Stratification

data/table

Evaluation of key non-covalent protein-ligand interactions (Hydrogen Bond Donors, Hydrogen Bond Acceptors, van der Waals contacts, and Hydrophobic interactions) using PoseCheck across size-stratified model groups on the CrossDocked benchmark. MolCRAFT forms the highest number of hydrogen bonds across all size tiers, confirming accurate physical interaction modeling rather than surface volume exploitation.

Size Tier	Methods	HB Donors (Avg.)	HB Acceptors (Avg.)	vdWs (Avg.)	Hydrophobic (Avg.)	Size (Avg.)
Reference	Reference	0.87	1.42	6.61	5.06	22.8
Smaller-size	AR	0.51	0.90	5.54	3.78	17.7
	Pocket2Mol	0.32	0.63	5.25	4.53	17.7
	FLAG	0.28	0.30	5.85	3.76	16.7
	Ours-small	0.62	1.09	6.24	4.42	17.8
Reference-size	TargetDiff	0.63	0.98	7.92	5.43	24.2
	Decomp-R	0.56	0.99	6.70	4.37	21.2
	Ours	0.71	1.25	7.38	5.07	22.7
Larger-size	Decomp-O	0.52	0.87	9.14	6.84	29.4
	Ours-large	0.75	1.38	8.64	6.07	29.4

Coverage note — Deliberately omitted individual per-bond-type and per-angle-type JSD breakdown tables (Tables 5-7) and baseline-specific prior preparation details (such as AlphaSpace2 pocket prior extraction for Decomp-O), retaining instead the aggregate substructural JSD benchmark and key failure analyses.

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Citation

MLA

Qu, Y., et al. “MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space”. arXiv, 2024, http://arxiv.org/abs/2404.12141v4.

APA

Qu, Y., Qiu, K., Song, Y., Gong, J., Han, J., Zheng, M., Zhou, H., & Ma, W.-Y. (2024). MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space. arXiv. http://arxiv.org/abs/2404.12141v4

Chicago

Qu, Y., K. Qiu, Y. Song, et al. 2024. “MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space”. arXiv. http://arxiv.org/abs/2404.12141v4.

Harvard

Qu, Y. et al. (2024) “MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2404.12141v4.

Vancouver

1. Qu Y, Qiu K, Song Y, Gong J, Han J, Zheng M, Zhou H, Ma W-Y (2024) MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space. arXiv

BibTeX

@article{qu2024molcraft,
  title = {MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space},
  author = {Qu, Yanru and Qiu, Keyue and Song, Yuxuan and Gong, Jingjing and Han, Jiawei and Zheng, Mingyue and Zhou, Hao and Ma, Wei-Ying},
  year = {2024},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2404.12141v4},
  eprint = {2404.12141}
}

Metadata:arXiv

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MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space

Abstract

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Table of Contents

Knowls

Knowl 1 — MolCRAFT Unified Parameter Space for Continuous Coordinates and Discrete Atom Types

Knowl 2 — MolCRAFT Noise-Reduced Sampling in Continuous Parameter Space

Knowl 3 — MolCRAFT Discrete-Time Training Objective and Loss Formulation

Knowl 4 — SE(3) Invariance of Likelihood and SE(3) Equivariant Coordinate Sampling

Knowl 5 — MolCRAFT SE(3)-Equivariant PosNet3D Backbone and Graph Featurization