# DiffER: Categorical Diffusion for Chemical Retrosynthesis

arXiv: https://arxiv.org/abs/2505.23721 · HTML: https://mlsanity.com/paper/2505.23721/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 29 May 2025.

## 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, 27 of 27)

- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models](https://mlsanity.com/paper/2211.15029/) (2022)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [Learning to Plan Chemical Syntheses](https://mlsanity.com/paper/1708.04202/) (2017)
- [Retrosynthesis Prediction with Conditional Graph Logic Network](https://mlsanity.com/paper/2001.01408/) (2020)
- [Molecule Edit Graph Attention Network: Modeling Chemical Reactions as Sequences of Graph Edits](https://mlsanity.com/paper/2006.15426/) (2020)
- [Retrosynthetic reaction prediction using neural sequence-to-sequence models](https://mlsanity.com/paper/1706.01643/) (2017)
- [A Graph to Graphs Framework for Retrosynthesis Prediction](https://mlsanity.com/paper/2003.12725/) (2020)
- [RetroXpert: Decompose Retrosynthesis Prediction like a Chemist](https://mlsanity.com/paper/2011.02893/) (2020)
- [Permutation invariant graph-to-sequence model for template-free retrosynthesis and reaction prediction](https://mlsanity.com/paper/2110.09681/) (2021)
- [Learning Graph Models for Retrosynthesis Prediction](https://mlsanity.com/paper/2006.07038/) (2020)
- [SeqDiffuSeq: Text Diffusion with Encoder-Decoder Transformers](https://mlsanity.com/paper/2212.10325/) (2022)
- [Root-aligned SMILES: A Tight Representation for Chemical Reaction Prediction](https://mlsanity.com/paper/2203.11444/) (2022)
- [DiffuSeq-v2: Bridging Discrete and Continuous Text Spaces for Accelerated Seq2Seq Diffusion Models](https://mlsanity.com/paper/2310.05793/) (2023)
- [GDiffRetro: Retrosynthesis Prediction with Dual Graph Enhanced Molecular Representation and Diffusion Generation](https://mlsanity.com/paper/2501.08001/) (2025)

## Abstract (arXiv)

Methods for automatic chemical retrosynthesis have found recent success through the application of models traditionally built for natural language processing, primarily through transformer neural networks. These models have demonstrated significant ability to translate between the SMILES encodings of chemical products and reactants, but are constrained as a result of their autoregressive nature. We propose DiffER, an alternative template-free method for retrosynthesis prediction in the form of categorical diffusion, which allows the entire output SMILES sequence to be predicted in unison. We construct an ensemble of diffusion models which achieves state-of-the-art performance for top-1 accuracy and competitive performance for top-3, top-5, and top-10 accuracy among template-free methods. We prove that DiffER is a strong baseline for a new class of template-free model, capable of learning a variety of synthetic techniques used in laboratory settings and outperforming a variety of other template-free methods on top-k accuracy metrics. By constructing an ensemble of categorical diffusion models with a novel length prediction component with variance, our method is able to approximately sample from the posterior distribution of reactants, producing results with strong metrics of confidence and likelihood. Furthermore, our analyses demonstrate that accurate prediction of the SMILES sequence length is key to further boosting the performance of categorical diffusion models.