# ContinualFlow: Learning and Unlearning with Neural Flow Matching

arXiv: https://arxiv.org/abs/2506.18747 · HTML: https://mlsanity.com/paper/2506.18747/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 16 of its 21 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)
- LLM safety and security / [Vision-language and text-to-image safety](https://mlsanity.com/safety/vision-language-and-text-to-image-safety/)

## Builds on (most cited first, 16 of 16)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models](https://mlsanity.com/paper/2211.05105/) (2022)
- [Unified Concept Editing in Diffusion Models](https://mlsanity.com/paper/2308.14761/) (2023)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [Rethinking Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2402.08787/) (2024)
- [Selective Amnesia: A Continual Learning Approach to Forgetting in Deep Generative Models](https://mlsanity.com/paper/2305.10120/) (2023)
- [Defensive Unlearning with Adversarial Training for Robust Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2405.15234/) (2024)
- [Understanding Hallucinations in Diffusion Models through Mode Interpolation](https://mlsanity.com/paper/2406.09358/) (2024)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [ReLearn: Unlearning via Learning for Large Language Models](https://mlsanity.com/paper/2502.11190/) (2025)
- [Continual Unlearning for Foundational Text-to-Image Models without Generalization Erosion](https://mlsanity.com/paper/2503.13769/) (2025)

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

- [Mosaic: Compositional Multi-Concept Erasure via Vector Field Blending](https://mlsanity.com/paper/2605.25574/) (2026)
- [Data Unlearning via Inverse Distillation](https://mlsanity.com/paper/2609.36099/) (2026)
- [Enabling Preference-driven Unlearning in Few-step Distilled Text-to-Image Diffusion Models](https://mlsanity.com/paper/2610.10859/) (2026)

## Abstract (arXiv)

We introduce ContinualFlow, a principled framework for targeted unlearning in generative models via Flow Matching. Our method leverages an energy-based reweighting loss to softly subtract undesired regions of the data distribution without retraining from scratch or requiring direct access to the samples to be unlearned. Instead, it relies on energy-based proxies to guide the unlearning process. We prove that this induces gradients equivalent to Flow Matching toward a soft mass-subtracted target, and validate the framework through experiments on 2D and image domains, supported by interpretable visualizations and quantitative evaluations.