# Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models

arXiv: https://arxiv.org/abs/2501.08727 · HTML: https://mlsanity.com/paper/2501.08727/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 78 references that are in the map.
- First posted on arXiv 15 Jan 2025.

## Builds on (most cited first, 30 of 56)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [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)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [T2I-Adapter: Learning Adapters to Dig out More Controllable Ability for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.08453/) (2023)
- [Multi-Concept Customization of Text-to-Image Diffusion](https://mlsanity.com/paper/2212.04488/) (2022)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [How far are we from solving the 2D & 3D Face Alignment problem? (and a dataset of 230,000 3D facial landmarks)](https://mlsanity.com/paper/1703.07332/) (2017)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [Mix-of-Show: Decentralized Low-Rank Adaptation for Multi-Concept Customization of Diffusion Models](https://mlsanity.com/paper/2305.18292/) (2023)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [RAPHAEL: Text-to-Image Generation via Large Mixture of Diffusion Paths](https://mlsanity.com/paper/2305.18295/) (2023)
- [FacT: Factor-Tuning for Lightweight Adaptation on Vision Transformer](https://mlsanity.com/paper/2212.03145/) (2022)

## Built on by (most cited first, 3 of 3)

- [Selecting Fine-Tuning Examples by Quizzing VLMs](https://mlsanity.com/paper/2511.12002/) (2025)
- [Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applications](https://mlsanity.com/paper/2512.23917/) (2025)
- [GLT-PEFT: Gated Lie-Tucker Parameter-Efficient Fine-Tuning for Alzheimer's Disease Diagnosis with Hippocampal Segmentation Pretraining](https://mlsanity.com/paper/2605.16769/) (2026)

## Abstract (arXiv)

Parameter-Efficient Fine-Tuning (PEFT) of text-to-image models has become an increasingly popular technique with many applications. Among the various PEFT methods, Low-Rank Adaptation (LoRA) and its variants have gained significant attention due to their effectiveness, enabling users to fine-tune models with limited computational resources. However, the approximation gap between the low-rank assumption and desired fine-tuning weights prevents the simultaneous acquisition of ultra-parameter-efficiency and better performance. To reduce this gap and further improve the power of LoRA, we propose a new PEFT method that combines two classes of adaptations, namely, transform and residual adaptations. In specific, we first apply a full-rank and dense transform to the pre-trained weight. This learnable transform is expected to align the pre-trained weight as closely as possible to the desired weight, thereby reducing the rank of the residual weight. Then, the residual part can be effectively approximated by more compact and parameter-efficient structures, with a smaller approximation error. To achieve ultra-parameter-efficiency in practice, we design highly flexible and effective tensor decompositions for both the transform and residual adaptations. Additionally, popular PEFT methods such as DoRA can be summarized under this transform plus residual adaptation scheme. Experiments are conducted on fine-tuning Stable Diffusion models in subject-driven and controllable generation. The results manifest that our method can achieve better performances and parameter efficiency compared to LoRA and several baselines.