In particular, torsional diffusion does not address the longstanding difficulty that existing cheminformatics methods have with macrocycles--rings with 12 or more atoms that have found several applications in drug discovery [Driggers et al., 2008].

Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular geometry elements (e.g., torsion angles), separate optimization stages prone to error accumulation, and the need for structure fine-tuning based on approximate classical force-fields or computationally expensive methods. We propose GEOMOL --- an end-to-end, non-autoregressive, and SE(3)-invariant machine learning approach to generate distributions of low-energy molecular 3D conformers. Leveraging the power of message passing neural networks (MPNNs) to capture local and global graph information, we predict local atomic 3D structures and torsion angles, avoiding unnecessary over-parameterization of the geometric degrees of freedom (e.g., one angle per non-terminal bond). Such local predictions suffice both for both the training loss computation and for the full deterministic conformer assembly (at test time). We devise a non-adversarial optimal transport based loss function to promote diverse conformer generation. GEOMOL predominantly outperforms popular open-source, commercial, or state-of-the-art machine learning (ML) models, while achieving significant speed-ups. We expect such differentiable 3D structure generators to significantly impact molecular modeling and related applications.

Designing new protein structures is fundamental to computational biology, enabling advances in therapeutic molecule discovery and enzyme engineering. Existing diffusion-based generative models typically operate in Cartesian coordinate space, where adding noise disrupts strict geometric constraints such as fixed bond lengths and angles, often producing physically invalid structures. To address this limitation, we propose a Torsion-Space Diffusion Model that generates protein backbones by denoising torsion angles, ensuring perfect local geometry by construction. A differentiable forward-kinematics module reconstructs 3D coordinates with fixed 3.8 Angstrom backbone bond lengths while a constrained post-processing refinement optimizes global compactness via Radius of Gyration (Rg) correction, without violating bond constraints. Experiments on standard PDB proteins demonstrate 100% bond-length accuracy and significantly improved structural compactness, reducing Rg error from 70% to 18.6% compared to Cartesian diffusion baselines. Overall, this hybrid torsion-diffusion plus geometric-refinement framework generates physically valid and compact protein backbones, providing a promising path toward full-atom protein generation.

Diffusion and flow matching models have recently emerged as promising approaches for peptide binder design. Despite their progress, these models still face two major challenges. First, categorical sampling of discrete residue types collapses their continuous parameters into onehot assignments, while continuous variables (e.g., atom positions) evolve smoothly throughout the generation process. This mismatch disrupts the update dynamics and results in suboptimal performance. Second, current models assume unimodal distributions for side-chain torsion angles, which conflicts with the inherently multimodal nature of side chain rotameric states and limits prediction accuracy. To address these limitations, we introduce PepBFN, the first Bayesian flow network for full atom peptide design that directly models parameter distributions in fully continuous space. Specifically, PepBFN models discrete residue types by learning their continuous parameter distributions, enabling joint and smooth Bayesian updates with other continuous structural parameters. It further employs a novel Gaussian mixture based Bayesian flow to capture the multimodal side chain rotameric states and a Matrix Fisher based Riemannian flow to directly model residue orientations on the $\mathrm{SO}(3)$ manifold. Together, these parameter distributions are progressively refined via Bayesian updates, yielding smooth and coherent peptide generation. Experiments on side chain packing, reverse folding, and binder design tasks demonstrate the strong potential of PepBFN in computational peptide design.

Molecular conformer generation is a fundamental task in computational chemistry. Several machine learning approaches have been developed, but none have outperformed state-of-the-art cheminformatics methods.

Peptide drugs incorporating non-standard amino acids (NSAAs) offer improved binding affinity and improved pharmacological properties. However, existing peptide design methods are limited to standard amino acids, leaving NSAA-aware design largely unexplored. We introduce NS-Pep, a unified framework for co-designing peptide sequences and structures with NSAAs. The main challenge is that NSAAs are extremely underrepresented-even the most frequent one, SEP, accounts for less than 0.4% of residues-resulting in a severe long-tailed distribution. To improve generalization to rare amino acids, we propose Residue Frequency-Guided Modification (RFGM), which mitigates over-penalization through frequency-aware logit calibration, supported by both theoretical and empirical analysis. Furthermore, we identify that insufficient side-chain modeling limits geometric representation of NSAAs. To address this, we introduce Progressive Side-chain Perception (PSP) for coarse-to-fine torsion and location prediction, and Interaction-Aware Weighting (IAW) to emphasize pocket-proximal residues. Moreover, NS-Pep generalizes naturally to the peptide folding task with NSAAs, addressing a major limitation of current tools. Experiments show that NS-Pep improves sequence recovery rate and binding affinity by 6.23% and 5.12%, respectively, and outperforms AlphaFold3 by 17.76% in peptide folding success rate.

Designing metal-organic frameworks (MOFs) with novel chemistries is a longstanding challenge due to their large combinatorial space and complex 3D arrangements of the building blocks. While recent deep generative models have enabled scalable MOF generation, they assume (1) a fixed set of building blocks and (2) known local 3D coordinates of building blocks. However, this limits their ability to (1) design novel MOFs and (2) generate the structure using novel building blocks. We propose a two-stage MOF generation framework that overcomes these limitations by modeling both chemical and geometric degrees of freedom. First, we train an SMILES-based autoregressive model to generate metal and organic building blocks, paired with a cheminformatics toolkit for 3D structure initialization. Second, we introduce a flow matching model that predicts translations, rotations, and torsional angles to assemble the blocks into valid 3D frameworks. Our experiments demonstrate improved reconstruction accuracy, the generation of valid, novel, and unique MOFs, and the ability to create novel building blocks. Our code is available at https://github.com/nayoung10/MOFFlow-2.