# Generative Pseudo-Force Fields for Molecular Generation

arXiv: https://arxiv.org/abs/2605.19050 · HTML: https://mlsanity.com/paper/2605.19050/

## Key facts

- Cited by 1 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 53 of its 101 references that are in the map.
- First posted on arXiv 18 May 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, 30 of 53)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [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)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [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)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)

## Built on by (most cited first, 1 of 1)

- [Representations from Pretrained Machine-Learning Interatomic Potentials as Coarse Coordinates for Material Generation and Evaluation](https://mlsanity.com/paper/2607.28776/) (2026)

## Abstract (arXiv)

Generating stable molecular conformations typically forces a tradeoff between the physical realism of energy-based relaxation and the sampling efficiency of data-driven generative models. While machine learning force fields (MLFFs) can sample stable conformations by relaxing molecular geometries according to physical forces, they require costly ab-initio training data. Conversely, diffusion models (DMs) learn from equilibrium data alone but are dependent on noise schedules and time-step conditioning. In this work, we propose generative pseudo-force fields (GPFFs) to bridge these paradigms by training an MLFF on a quadratic pseudo-potential energy surface relative to reference equilibrium structures. Because no ab-initio calculations are required for the perturbed geometries, non-equilibrium training data can be generated on the fly by perturbing the equilibria with Gaussian noise. We show that GPFFs constitute a time-step-agnostic variant of variance exploding DMs: the score comes from the predicted pseudo-forces but because force magnitudes implicitly encode the noise level, no time-step conditioning is needed. Our GPFF can hence be used as a drop-in replacement in standard diffusion sampling (ancestral, Heun) but also facilitates more efficient, adaptive variants and an MLFF inspired direct denoising scheme. Our proposed sampling algorithms support arbitrary structural priors and geometric constraints. On QM9, GPFF has 100 % validity at 256 neural function evaluations (NFE) and over 50 % at just 6 NFE, outperforming diffusion baselines across all samplers. Combined with custom priors, we showcase the fast and accurate generation process of our method in a molecular editor for a drug design setting, where a molecule is generated in real time.