# Chemistry-Inspired Diffusion with Non-Differentiable Guidance

arXiv: https://arxiv.org/abs/2410.06502 · HTML: https://mlsanity.com/paper/2410.06502/

## Key facts

- Cited by 6 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 35 of its 55 references that are in the map.
- First posted on arXiv 9 Oct 2024.

## 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, 30 of 35)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)
- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)

## Built on by (most cited first, 6 of 6)

- [Evolvable Conditional Diffusion](https://mlsanity.com/paper/2506.13834/) (2025)
- [Tree-Guided Diffusion Planner](https://mlsanity.com/paper/2508.21800/) (2025)
- [Elign: Equivariant Diffusion Model Alignment from Foundational Machine Learning Force Fields](https://mlsanity.com/paper/2601.21985/) (2026)
- [Diffusion Models with Double Guidance: Generate with aggregated datasets](https://mlsanity.com/paper/2505.13213/) (2025)
- [Learning from B Cell Evolution: Adaptive Multi-Expert Diffusion for Antibody Design via Online Optimization](https://mlsanity.com/paper/2508.02834/) (2025)
- [RIDE: Reference-Anchored Inference-Time Diffusion Editing for Scaffold Hopping](https://mlsanity.com/paper/2609.35623/) (2026)

## Abstract (arXiv)

Recent advances in diffusion models have shown remarkable potential in the conditional generation of novel molecules. These models can be guided in two ways: (i) explicitly, through additional features representing the condition, or (ii) implicitly, using a property predictor. However, training property predictors or conditional diffusion models requires an abundance of labeled data and is inherently challenging in real-world applications. We propose a novel approach that attenuates the limitations of acquiring large labeled datasets by leveraging domain knowledge from quantum chemistry as a non-differentiable oracle to guide an unconditional diffusion model. Instead of relying on neural networks, the oracle provides accurate guidance in the form of estimated gradients, allowing the diffusion process to sample from a conditional distribution specified by quantum chemistry. We show that this results in more precise conditional generation of novel and stable molecular structures. Our experiments demonstrate that our method: (1) significantly reduces atomic forces, enhancing the validity of generated molecules when used for stability optimization; (2) is compatible with both explicit and implicit guidance in diffusion models, enabling joint optimization of molecular properties and stability; and (3) generalizes effectively to molecular optimization tasks beyond stability optimization.