# FRIGID: Scaling Diffusion-Based Molecular Generation from Mass Spectra at Training and Inference Time

arXiv: https://arxiv.org/abs/2604.16648 · HTML: https://mlsanity.com/paper/2604.16648/

## Key facts

- Cited by 4 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 19 of its 49 references that are in the map.
- First posted on arXiv 17 Apr 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, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [GenMol: A Drug Discovery Generalist with Discrete Diffusion](https://mlsanity.com/paper/2501.06158/) (2025)
- [Gotta be SAFE: A New Framework for Molecular Design](https://mlsanity.com/paper/2310.10773/) (2023)
- [DiffMS: Diffusion Generation of Molecules Conditioned on Mass Spectra](https://mlsanity.com/paper/2502.09571/) (2025)
- [Unraveling Molecular Structure: A Multimodal Spectroscopic Dataset for Chemistry](https://mlsanity.com/paper/2407.17492/) (2024)
- [MADGEN: Mass-Spec attends to De Novo Molecular generation](https://mlsanity.com/paper/2501.01950/) (2025)
- [Fragmentation trees reloaded](https://mlsanity.com/paper/1412.1929/) (2014)
- [Test-Time Tuned Language Models Enable End-to-end De Novo Molecular Structure Generation from MS/MS Spectra](https://mlsanity.com/paper/2510.23746/) (2025)
- [Generative structural elucidation from mass spectra as an iterative optimization problem](https://mlsanity.com/paper/2602.07709/) (2026)

## Built on by (most cited first, 4 of 4)

- [MassSpecGym in the Wild: Uncovering and Correcting Evaluation Pitfalls in AI-Driven Molecule Discovery](https://mlsanity.com/paper/2606.19624/) (2026)
- [MARLIN: De Novo Molecular Structure Elucidation from Tandem Mass Spectra without a Ground-Truth Formula](https://mlsanity.com/paper/2607.04774/) (2026)
- [MS-GPT: Rethinking MS/MS De Novo Structure Elucidation as Spectrum-Induced Posterior Querying of a Molecule-Language Model](https://mlsanity.com/paper/2607.23607/) (2026)
- [Critical Mass: Structure-Disjoint Splits Drift With the Libraries They Are Built On](https://mlsanity.com/paper/2610.12694/) (2026)

## Abstract (arXiv)

Tandem mass spectrometry is prominent in scientific discovery workflows for identifying unknown small molecules, yet high-throughput structural elucidation remains challenging. While recent autoregressive and graph diffusion models have shown promise in de novo elucidation, performance remains limited by poor scalability during both training and inference time. In this work, we present FRIGID, a framework with a novel diffusion language model that generates molecular structures conditioned on mass spectra via intermediate fingerprint representations and determined chemical formulae, training at the scale of hundreds of millions of unlabeled structures. We then demonstrate how forward fragmentation models enable inference-time scaling by identifying spectrum-inconsistent fragments and refining them through targeted remasking and denoising. While FRIGID already achieves strong performance with its diffusion base, inference-time scaling significantly improves its accuracy, surpassing 18% Top-1 accuracy on the challenging MassSpecGym benchmark and tripling the Top-1 accuracy of the leading methods on NPLIB1. Further empirical analyses show that FRIGID exhibits log-linear performance scaling with increasing inference-time compute, opening a promising new direction for continued improvements in de novo structural elucidation. FRIGID code is publicly available at https://github.com/coleygroup/FRIGID.