# MING: A Functional Approach to Learning Molecular Generative Models

arXiv: https://arxiv.org/abs/2410.12522 · HTML: https://mlsanity.com/paper/2410.12522/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 29 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [Learning Signal-Agnostic Manifolds of Neural Fields](https://mlsanity.com/paper/2111.06387/) (2021)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [Diffusion Probabilistic Fields](https://mlsanity.com/paper/2303.00165/) (2023)
- [Manifold Diffusion Fields](https://mlsanity.com/paper/2305.15586/) (2023)
- [Gradient Origin Networks](https://mlsanity.com/paper/2007.02798/) (2020)
- [Variational Mixture of HyperGenerators for Learning Distributions Over Functions](https://mlsanity.com/paper/2302.06223/) (2023)

## Abstract (arXiv)

Traditional molecule generation methods often rely on sequence- or graph-based representations, which can limit their expressive power or require complex permutation-equivariant architectures. This paper introduces a novel paradigm for learning molecule generative models based on functional representations. Specifically, we propose Molecular Implicit Neural Generation (MING), a diffusion-based model that learns molecular distributions in the function space. Unlike standard diffusion processes in the data space, MING employs a novel functional denoising probabilistic process, which jointly denoises information in both the function's input and output spaces by leveraging an expectation-maximization procedure for latent implicit neural representations of data. This approach enables a simple yet effective model design that accurately captures underlying function distributions. Experimental results on molecule-related datasets demonstrate MING's superior performance and ability to generate plausible molecular samples, surpassing state-of-the-art data-space methods while offering a more streamlined architecture and significantly faster generation times. The code is available at https://github.com/v18nguye/MING.