# Unlocking the Potential of Continual Model Merging: An ODE Perspective

arXiv: https://arxiv.org/abs/2605.19409 · HTML: https://mlsanity.com/paper/2605.19409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 30 of 34)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (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)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Challenges in Representation Learning: A report on three machine learning contests](https://mlsanity.com/paper/1307.0414/) (2013)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Deep Model Fusion: A Survey](https://mlsanity.com/paper/2309.15698/) (2023)
- [Model Merging by Uncertainty-Based Gradient Matching](https://mlsanity.com/paper/2310.12808/) (2023)
- [Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer](https://mlsanity.com/paper/2211.00789/) (2022)
- [What Matters for Model Merging at Scale?](https://mlsanity.com/paper/2410.03617/) (2024)
- [A Survey on Model MoErging: Recycling and Routing Among Specialized Experts for Collaborative Learning](https://mlsanity.com/paper/2408.07057/) (2024)
- [Model Merging and Safety Alignment: One Bad Model Spoils the Bunch](https://mlsanity.com/paper/2406.14563/) (2024)
- [The Emergence of Essential Sparsity in Large Pre-trained Models: The Weights that Matter](https://mlsanity.com/paper/2306.03805/) (2023)
- [Activation-Informed Merging of Large Language Models](https://mlsanity.com/paper/2502.02421/) (2025)
- [Merging Models on the Fly Without Retraining: A Sequential Approach to Scalable Continual Model Merging](https://mlsanity.com/paper/2501.09522/) (2025)
- [Merging Vision Transformers from Different Tasks and Domains](https://mlsanity.com/paper/2312.16240/) (2023)
- [Mitigating Parameter Interference in Model Merging via Sharpness-Aware Fine-Tuning](https://mlsanity.com/paper/2504.14662/) (2025)
- [Training-Free Model Merging for Multi-target Domain Adaptation](https://mlsanity.com/paper/2407.13771/) (2024)
- [FusionBench: A Unified Library and Comprehensive Benchmark for Deep Model Fusion](https://mlsanity.com/paper/2406.03280/) (2024)

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

- [From Parameters to Behaviors: A Survey of Model Fusion for Large Language Models](https://mlsanity.com/paper/2609.19553/) (2026)

## Abstract (arXiv)

Continual Model Merging (CMM) enables rapid customization of foundation models by sequentially incorporating task-adapted models without repeated retraining. However, existing merging rules usually update the deployed model through fixed algebraic or projection-based operations, providing limited control over how much previously accumulated knowledge should be retained relative to the incoming task model. This limitation leads to unstable retention and performance degradation in long task streams, and becomes more pronounced when tasks have heterogeneous utilities. We propose ODE-driven Merging (ODE-M), a controllable framework that formulates each continual merge as a trajectory in parameter space rather than a one-step endpoint update. Motivated by mode connectivity, ODE-M constructs a barrier-aware trajectory using a rectified time-dependent velocity field, where lightweight first-order feedback from a small calibration set suppresses loss-increasing motion while preserving progress toward the incoming model. The next merged model is then obtained by selecting an operating point along this trajectory through a utility-aware time schedule, providing an explicit mechanism for balancing retained historical knowledge and incoming task expertise. Extensive experiments on standard CMM benchmarks show that ODE-M consistently improves over strong continual merging baselines across CLIP ViT backbones, stream lengths, and heterogeneous task-utility settings.