# Fast Organic Crystal Structure Prediction with Unit Cell Flow Matching

arXiv: https://arxiv.org/abs/2606.03199 · HTML: https://mlsanity.com/paper/2606.03199/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 99 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Proteina: Scaling Flow-based Protein Structure Generative Models](https://mlsanity.com/paper/2503.00710/) (2025)

## Built on by (most cited first, 3 of 3)

- [OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery](https://mlsanity.com/paper/2609.26402/) (2026)
- [Packora: Systematic Design for Generative Molecular Crystal Structure Prediction](https://mlsanity.com/paper/2608.26962/) (2026)
- [Where Should Physics Enter a Molecular Crystal Generator?](https://mlsanity.com/paper/2609.36398/) (2026)

## Abstract (arXiv)

Organic crystal structure prediction (CSP) is a requirement for computational modelling of organic solids, but traditionally costs several CPU-years per molecule. Generative models such as OXtal dramatically reduce this cost by sampling stable organic crystal structures directly. However, OXtal forgoes explicit lattice parametrization in favour of modelling large crops of the bulk material with expensive triangle layers, which can incur a computational cost of minutes per molecule. In this paper, we reduce this to seconds with Clari, a large-scale flow matching model that generates redundancy-free unit cells and replaces triangle layers with pure pair-bias attention. Clari requires only atom types and bonds as input and does not need an RDKit-sanitizable input molecule, which expands its applicability to challenging chemistries such as fullerenes, metal complexes, and atom clusters. We further ablate key design choices such as auxiliary losses, timestep distributions, noise priors, and self-conditioning. On OXtal's test sets, we surpass OXtal's solve rate while obtaining a speedup of 15-30×. Because Clari also models explicit hydrogens, it supports inference-time scaling via direct energy ranking, without any decoration or relaxation step. When generating 150 crystals and selecting the top-30 by energy, we further improve solve rate while maintaining a speedup of 5-8×. We also introduce the CSD Teaching Subset as a new test split of diverse and complex molecules for future benchmarking. Our contributions enable CSP within seconds, making large-scale virtual screening of organic solids practical. Code is available at https://github.com/aspuru-guzik-group/clari.