# FouRA: Fourier Low Rank Adaptation

arXiv: https://arxiv.org/abs/2406.08798 · HTML: https://mlsanity.com/paper/2406.08798/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 35 of its 48 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 30 of 35)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
- [Multi-Concept Customization of Text-to-Image Diffusion](https://mlsanity.com/paper/2212.04488/) (2022)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Mix-of-Show: Decentralized Low-Rank Adaptation for Multi-Concept Customization of Diffusion Models](https://mlsanity.com/paper/2305.18292/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Understanding and Mitigating Copying in Diffusion Models](https://mlsanity.com/paper/2305.20086/) (2023)
- [FreeU: Free Lunch in Diffusion U-Net](https://mlsanity.com/paper/2309.11497/) (2023)
- [ZipLoRA: Any Subject in Any Style by Effectively Merging LoRAs](https://mlsanity.com/paper/2311.13600/) (2023)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [Concept Sliders: LoRA Adaptors for Precise Control in Diffusion Models](https://mlsanity.com/paper/2311.12092/) (2023)
- [On the Effectiveness of Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2211.15583/) (2022)
- [Uncovering the Disentanglement Capability in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2212.08698/) (2022)
- [Sparse Low-rank Adaptation of Pre-trained Language Models](https://mlsanity.com/paper/2311.11696/) (2023)
- [Multi-LoRA Composition for Image Generation](https://mlsanity.com/paper/2402.16843/) (2024)

## Built on by (most cited first, 15 of 15)

- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [LoRA-X: Bridging Foundation Models with Training-Free Cross-Model Adaptation](https://mlsanity.com/paper/2501.16559/) (2025)
- [Exploring Sparsity for Parameter Efficient Fine Tuning Using Wavelets for Vision](https://mlsanity.com/paper/2505.12532/) (2025)
- [MultLFG: Training-free Multi-LoRA composition using Frequency-domain Guidance](https://mlsanity.com/paper/2505.20525/) (2025)
- [Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models](https://mlsanity.com/paper/2501.08727/) (2025)
- [SubZero: Composing Subject, Style, and Action via Zero-Shot Personalization](https://mlsanity.com/paper/2502.19673/) (2025)
- [AdaptSR: Low-Rank Adaptation for Efficient and Scalable Real-World Super-Resolution](https://mlsanity.com/paper/2503.07748/) (2025)
- [Meta-LoRA: Meta-Learning LoRA Components for Domain-Aware ID Personalization](https://mlsanity.com/paper/2503.22352/) (2025)
- [WaRA: Wavelet Low-Rank Adaptation for Medical Image Classification](https://mlsanity.com/paper/2506.24092/) (2025)
- [Diving into Kronecker Adapters: Component Design Matters](https://mlsanity.com/paper/2602.01267/) (2026)
- [SpiralDiff: Spiral Diffusion with LoRA for RGB-to-RAW Conversion Across Cameras](https://mlsanity.com/paper/2603.14885/) (2026)
- [Leveraging Image Editing Foundation Models for Data-Efficient CT Metal Artifact Reduction](https://mlsanity.com/paper/2604.05934/) (2026)
- [LoRA-Diffusion: Parameter-Efficient Fine-Tuning via Low-Rank Trajectory Decomposition](https://mlsanity.com/paper/2608.12328/) (2026)
- [Frequency-Aware Continual Learning for Smart Contract Vulnerability Detection with Large Language Models](https://mlsanity.com/paper/2608.19680/) (2026)
- [Behavior Quotient Learning for Low-Rank Adaptation of LLM Agents](https://mlsanity.com/paper/2609.12896/) (2026)

## Abstract (arXiv)

While Low-Rank Adaptation (LoRA) has proven beneficial for efficiently fine-tuning large models, LoRA fine-tuned text-to-image diffusion models lack diversity in the generated images, as the model tends to copy data from the observed training samples. This effect becomes more pronounced at higher values of adapter strength and for adapters with higher ranks which are fine-tuned on smaller datasets. To address these challenges, we present FouRA, a novel low-rank method that learns projections in the Fourier domain along with learning a flexible input-dependent adapter rank selection strategy. Through extensive experiments and analysis, we show that FouRA successfully solves the problems related to data copying and distribution collapse while significantly improving the generated image quality. We demonstrate that FouRA enhances the generalization of fine-tuned models thanks to its adaptive rank selection. We further show that the learned projections in the frequency domain are decorrelated and prove effective when merging multiple adapters. While FouRA is motivated for vision tasks, we also demonstrate its merits for language tasks on the GLUE benchmark.