# Data Unlearning via Inverse Distillation

arXiv: https://arxiv.org/abs/2609.36099 · HTML: https://mlsanity.com/paper/2609.36099/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 45 of its 52 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)
- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 30 of 45)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Unified Concept Editing in Diffusion Models](https://mlsanity.com/paper/2308.14761/) (2023)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [MACE: Mass Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2403.06135/) (2024)
- [Forget-Me-Not: Learning to Forget in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.17591/) (2023)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [Selective Amnesia: A Continual Learning Approach to Forgetting in Deep Generative Models](https://mlsanity.com/paper/2305.10120/) (2023)
- [EraseAnything: Enabling Concept Erasure in Rectified Flow Transformers](https://mlsanity.com/paper/2412.20413/) (2024)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Erasing Undesirable Influence in Diffusion Models](https://mlsanity.com/paper/2401.05779/) (2024)
- [ConceptPrune: Concept Editing in Diffusion Models via Skilled Neuron Pruning](https://mlsanity.com/paper/2405.19237/) (2024)

## Abstract (arXiv)

Multi-step matching models, including flow and diffusion models, produce high-quality outputs but incur substantial inference costs and may reproduce unwanted components of their training datasets. We introduce Inverse Distillation Unlearning (IDU), a unified framework that simultaneously distills a teacher multi-step matching model into an efficient one-step student generator and suppresses outputs corresponding to a designated training subset. We first formulate distillation as a min-max objective over a data distribution and then represent this distribution as a mixture of the forget-set and the generated distributions. This allows us to compare this mixture with the teacher's training distribution and recover only the retained data at the optimum. Our method requires only a pretrained full-data teacher and data from the forget set, without access to retained training examples, extra feature extractors or classifiers. Extensive experiments on MNIST and CIFAR-10 datasets under flow-matching and score-based diffusion settings demonstrate that IDU substantially reduces the generation frequency of forgotten classes while preserving generation quality on the retained classes. To the best of our knowledge, IDU is the first unified framework for simultaneous unlearning and distillation in unconditional flow-matching and score-based models.