# Generating Cyclic Conformers with Flow Matching in Cremer-Pople Coordinates

arXiv: https://arxiv.org/abs/2601.12859 · HTML: https://mlsanity.com/paper/2601.12859/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 75 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [PPFlow: Target-aware Peptide Design with Torsional Flow Matching](https://mlsanity.com/paper/2405.06642/) (2024)
- [Accurate and Efficient Structural Ensemble Generation of Macrocyclic Peptides using Internal Coordinate Diffusion](https://mlsanity.com/paper/2305.19800/) (2023)

## Built on by (most cited first, 2 of 2)

- [MacroGuide: Topological Guidance for Macrocycle Generation](https://mlsanity.com/paper/2602.14977/) (2026)
- [Manifold Diffusion for Structure Generation of Transition Metal Complexes](https://mlsanity.com/paper/2606.00666/) (2026)

## Abstract (arXiv)

Cyclic molecules are ubiquitous across applications in chemistry and biology. Their restricted conformational flexibility provides structural pre-organization that is key to their function in drug discovery and catalysis. However, reliably sampling the conformer ensembles of ring systems remains challenging. Here, we introduce PuckerFlow, a generative machine learning model that performs flow matching on the Cremer-Pople space, a low-dimensional internal coordinate system capturing the relevant degrees of freedom of rings. Our approach enables generation of valid closed rings by design and demonstrates strong performance in generating conformers that are both diverse and precise. We show that PuckerFlow outperforms other conformer generation methods on nearly all quantitative metrics and illustrate the potential of PuckerFlow for ring systems relevant to chemical applications, particularly in catalysis and drug discovery. This work enables efficient and reliable conformer generation of cyclic structures, paving the way towards modeling structure-property relationships and the property-guided generation of rings across a wide range of applications in chemistry and biology.