# SDO: Subspace Deconflicting Operator for Multi-Adapter Composition

arXiv: https://arxiv.org/abs/2608.13820 · HTML: https://mlsanity.com/paper/2608.13820/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [Cross-stitch Networks for Multi-task Learning](https://mlsanity.com/paper/1604.03539/) (2016)
- [BLIP-Diffusion: Pre-trained Subject Representation for Controllable Text-to-Image Generation and Editing](https://mlsanity.com/paper/2305.14720/) (2023)
- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [PhotoMaker: Customizing Realistic Human Photos via Stacked ID Embedding](https://mlsanity.com/paper/2312.04461/) (2023)
- [Domain Separation Networks](https://mlsanity.com/paper/1608.06019/) (2016)
- [FastComposer: Tuning-Free Multi-Subject Image Generation with Localized Attention](https://mlsanity.com/paper/2305.10431/) (2023)
- [Key-Locked Rank One Editing for Text-to-Image Personalization](https://mlsanity.com/paper/2305.01644/) (2023)
- [MS-Diffusion: Multi-subject Zero-shot Image Personalization with Layout Guidance](https://mlsanity.com/paper/2406.07209/) (2024)
- [Multi-LoRA Composition for Image Generation](https://mlsanity.com/paper/2402.16843/) (2024)
- [LoRA-Composer: Leveraging Low-Rank Adaptation for Multi-Concept Customization in Training-Free Diffusion Models](https://mlsanity.com/paper/2403.11627/) (2024)
- [Cached Multi-Lora Composition for Multi-Concept Image Generation](https://mlsanity.com/paper/2502.04923/) (2025)
- [ObjectComposer: Consistent Generation of Multiple Objects Without Fine-tuning](https://mlsanity.com/paper/2310.06968/) (2023)
- [CharCom: Composable Identity Control for Multi-Character Story Illustration](https://mlsanity.com/paper/2510.10135/) (2025)
- [Look, Compare and Draw: Differential Query Transformer for Automatic Oil Painting](https://mlsanity.com/paper/2603.27720/) (2026)

## Abstract (arXiv)

Composing independently trained adapters within a shared diffusion backbone provides a modular approach to multi-character generation, but naive joint deployment often causes identity mixing, cross-character attribute leakage, and unstable scene composition. We study this interference from a parameter-space perspective and hypothesize that it arises partly from conflicts between overlapping dominant subspaces in shared layers. To address this issue, we propose SDO, a Subspace Deconflicting Operator for multi-adapter composition. SDO reconstructs layer-wise low-rank updates from the selected adapters, extracts compact subspace signatures, measures pairwise conflict through output-subspace overlap, and applies a permutation-equivariant transformation that suppresses harmful shared directions while retaining identity-specific characteristics. The resulting representations are mapped back to standard adapter updates and can be directly incorporated into existing diffusion inference pipelines. Experiments demonstrate that SDO consistently improves identity fidelity and compositional stability, with particularly clear gains as the number of jointly composed adapters increases.