# Modeling Molecular Structures with Intrinsic Diffusion Models

arXiv: https://arxiv.org/abs/2302.12255 · HTML: https://mlsanity.com/paper/2302.12255/

## 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 32 of its 107 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## 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 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Noise Estimation for Generative Diffusion Models](https://mlsanity.com/paper/2104.02600/) (2021)
- [Progressive Distillation for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2202.00512/) (2022)
- [BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesis](https://mlsanity.com/paper/2203.13508/) (2022)

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

- [Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models](https://mlsanity.com/paper/2310.13102/) (2023)
- [Deep Confident Steps to New Pockets: Strategies for Docking Generalization](https://mlsanity.com/paper/2402.18396/) (2024)
- [DiffDock-PP: Rigid Protein-Protein Docking with Diffusion Models](https://mlsanity.com/paper/2304.03889/) (2023)
- [Evaluating representation learning on the protein structure universe](https://mlsanity.com/paper/2406.13864/) (2024)

## Abstract (arXiv)

Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However, a fundamental challenge with this approach has been the dynamic nature of these particles, which forces us to model not a single but a whole distribution of structures for every molecular system. This thesis proposes Intrinsic Diffusion Modeling, a novel approach to this problem based on combining diffusion generative models with scientific knowledge about the flexibility of biological complexes. The knowledge of these degrees of freedom is translated into the definition of a manifold over which the diffusion process is defined. This manifold significantly reduces the dimensionality and increases the smoothness of the generation space allowing for significantly faster and more accurate generative processes. We demonstrate the effectiveness of this approach on two fundamental tasks at the basis of computational chemistry and biology: molecular conformer generation and molecular docking. In both tasks, we construct the first deep learning method to outperform traditional computational approaches achieving an unprecedented level of accuracy for scalable programs.