GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters

2025-07-02

AI Summary

Geometric diffusion models struggle to simultaneously ensure geometric consistency, flexible controllability, and parameter efficiency in downstream tasks. Method: This paper proposes GeoAda, an SE(3)-equivariant adapter framework that fine-tunes pretrained backbones without architectural modification. It employs zero-initialized SE(3)-equivariant convolutions, structured coupling/decoupling operators, and control-signal encoding/decoding mechanisms to achieve lightweight, theoretically guaranteed SE(3) equivariance. Contribution/Results: GeoAda is the first to embed SE(3)-equivariance constraints directly into adapter design, jointly ensuring geometric consistency and expressive controllability. Layer replication and decoupling operations mitigate catastrophic forgetting and overfitting. Experiments demonstrate state-of-the-art performance across diverse tasks—including molecular dynamics, particle system simulation, and human motion prediction—under multiple control modalities, while fully preserving the original generative capabilities of the base model.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Efficiently fine-tune geometric diffusion models for downstream tasks
• Maintain SE(3)-equivariance during adaptation without architecture changes
• Address overfitting and catastrophic forgetting in controlled generative tasks

Innovation

• SE(3)-equivariant adapter framework for fine-tuning
• Lightweight structured adapter preserves geometric consistency
• Zero-initialized convolution ensures equivariance during adaptation