# GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters

arXiv: https://arxiv.org/abs/2507.02085 · HTML: https://mlsanity.com/paper/2507.02085/

## 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 36 of its 42 references that are in the map.
- First posted on arXiv 2 Jul 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, 30 of 36)

- [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)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [GraphPrompt: Unifying Pre-Training and Downstream Tasks for Graph Neural Networks](https://mlsanity.com/paper/2302.08043/) (2023)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [A 3D Generative Model for Structure-Based Drug Design](https://mlsanity.com/paper/2203.10446/) (2022)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)
- [In-Context Learning Unlocked for Diffusion Models](https://mlsanity.com/paper/2305.01115/) (2023)
- [MSR-GCN: Multi-Scale Residual Graph Convolution Networks for Human Motion Prediction](https://mlsanity.com/paper/2108.07152/) (2021)
- [Universal Prompt Tuning for Graph Neural Networks](https://mlsanity.com/paper/2209.15240/) (2022)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [Generating 3D Molecules Conditional on Receptor Binding Sites with Deep Generative Models](https://mlsanity.com/paper/2110.15200/) (2021)
- [SocialVAE: Human Trajectory Prediction using Timewise Latents](https://mlsanity.com/paper/2203.08207/) (2022)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)

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

- [Robust and Interpretable Adaptation of Equivariant Materials Foundation Models via Sparsity-promoting Fine-tuning](https://mlsanity.com/paper/2606.18691/) (2026)

## Abstract (arXiv)

Geometric diffusion models have shown remarkable success in molecular dynamics and structure generation. However, efficiently fine-tuning them for downstream tasks with varying geometric controls remains underexplored. In this work, we propose an SE(3)-equivariant adapter framework ( GeoAda) that enables flexible and parameter-efficient fine-tuning for controlled generative tasks without modifying the original model architecture. GeoAda introduces a structured adapter design: control signals are first encoded through coupling operators, then processed by a trainable copy of selected pretrained model layers, and finally projected back via decoupling operators followed by an equivariant zero-initialized convolution. By fine-tuning only these lightweight adapter modules, GeoAda preserves the model's geometric consistency while mitigating overfitting and catastrophic forgetting. We theoretically prove that the proposed adapters maintain SE(3)-equivariance, ensuring that the geometric inductive biases of the pretrained diffusion model remain intact during adaptation. We demonstrate the wide applicability of GeoAda across diverse geometric control types, including frame control, global control, subgraph control, and a broad range of application domains such as particle dynamics, molecular dynamics, human motion prediction, and molecule generation. Empirical results show that GeoAda achieves state-of-the-art fine-tuning performance while preserving original task accuracy, whereas other baselines experience significant performance degradation due to overfitting and catastrophic forgetting.