# Fixed-Dimensional Latent Flow for Generating Variable-Size 3D Molecules

arXiv: https://arxiv.org/abs/2609.08333 · HTML: https://mlsanity.com/paper/2609.08333/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 8 of 8)

- [Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2404.19739/) (2024)
- [Scalable Autoregressive 3D Molecule Generation](https://mlsanity.com/paper/2505.13791/) (2025)
- [Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation](https://mlsanity.com/paper/2602.15022/) (2026)
- [NEAT: Neighborhood-Guided, Efficient, Autoregressive Set Transformer for 3D Molecular Generation](https://mlsanity.com/paper/2512.05844/) (2025)
- [Frame-based Equivariant Diffusion Models for 3D Molecular Generation](https://mlsanity.com/paper/2509.19506/) (2025)
- [Permutation-Symmetrized Diffusion for Unconditional Molecular Generation](https://mlsanity.com/paper/2603.23255/) (2026)
- [DriftingMol: Decoder-Coupled Drift for One-Pass Property-Conditional Molecular Generation](https://mlsanity.com/paper/2605.24841/) (2026)
- [Autoregressive latent diffusion for 3D molecule generation](https://mlsanity.com/paper/2607.09277/) (2026)

## Built on by (most cited first, 1 of 1)

- [GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generation](https://mlsanity.com/paper/2609.37158/) (2026)

## Abstract (arXiv)

Molecular size is coupled to composition, structure, and function, yet most 3D molecular generators require a predefined atom count. We introduce Equivariant-Free Transformer-Autoencoded Latent Flow Matching, a two-stage framework that samples a fixed-dimensional latent vector using flow matching and uses an autoregressive Transformer to determine molecular size, atom types, coordinates, and chemical attributes. Canonical atom ordering and rigid-pose alignment enable Transformers without equivariant layers, while decoded attributes guide bond reconstruction. On PCQM4Mv2, unconditional generation yields 87.9% unique, novel molecules passing sanitization and PoseBusters checks, exceeding baselines with lower end-to-end training and sampling time and higher end-to-end throughput. Across ten target HOMO-LUMO gaps, internal ranking retains 30% of screened candidates and increases the density functional theory-verified hit rate within 0.1 eV from 25.0% to 52.4%, while largely preserving novelty and diversity. These results demonstrate fixed-dimensional latent generation with autoregressive decoding as a practical approach to molecular design without prespecifying size.