# Controllable Unlearning for Image-to-Image Generative Models via varepsilon-Constrained Optimization

arXiv: https://arxiv.org/abs/2408.01689 · HTML: https://mlsanity.com/paper/2408.01689/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Vision-language and text-to-image safety, one of 12 directions in LLM safety and security.
- Builds on 43 of its 73 references that are in the map.
- First posted on arXiv 3 Aug 2024.

## Placed in

- 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, 30 of 43)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)

## Built on by (most cited first, 5 of 5)

- [Are We Truly Forgetting? A Critical Re-examination of Machine Unlearning Evaluation Protocols](https://mlsanity.com/paper/2503.06991/) (2025)
- [Multimodal Unlearning Across Vision, Language, Video, and Audio: Survey of Methods, Datasets, and Benchmarks](https://mlsanity.com/paper/2607.07907/) (2026)
- [Generative Model Unlearning: A Survey through Target Events, Unlearning Operators, and Evaluation Protocols](https://mlsanity.com/paper/2507.19894/) (2025)
- [Realistic Image-to-Image Machine Unlearning via Decoupling and Knowledge Retention](https://mlsanity.com/paper/2502.04260/) (2025)
- [TOFA: Training-Free One-Shot Federated Adaptation for Vision-Language Models](https://mlsanity.com/paper/2511.16423/) (2025)

## Abstract (arXiv)

While generative models have made significant advancements in recent years, they also raise concerns such as privacy breaches and biases. Machine unlearning has emerged as a viable solution, aiming to remove specific training data, e.g., containing private information and bias, from models. In this paper, we study the machine unlearning problem in Image-to-Image (I2I) generative models. Previous studies mainly treat it as a single objective optimization problem, offering a solitary solution, thereby neglecting the varied user expectations towards the trade-off between complete unlearning and model utility. To address this issue, we propose a controllable unlearning framework that uses a control coefficient varepsilon to control the trade-off. We reformulate the I2I generative model unlearning problem into a varepsilon-constrained optimization problem and solve it with a gradient-based method to find optimal solutions for unlearning boundaries. These boundaries define the valid range for the control coefficient. Within this range, every yielded solution is theoretically guaranteed with Pareto optimality. We also analyze the convergence rate of our framework under various control functions. Extensive experiments on two benchmark datasets across three mainstream I2I models demonstrate the effectiveness of our controllable unlearning framework.