# Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraints

arXiv: https://arxiv.org/abs/2605.30825 · HTML: https://mlsanity.com/paper/2605.30825/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 39 of its 48 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)
- 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 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [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)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Selective Amnesia: A Continual Learning Approach to Forgetting in Deep Generative Models](https://mlsanity.com/paper/2305.10120/) (2023)
- [A Self-Supervised Descriptor for Image Copy Detection](https://mlsanity.com/paper/2202.10261/) (2022)
- [Defensive Unlearning with Adversarial Training for Robust Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2405.15234/) (2024)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [The Principles of Diffusion Models](https://mlsanity.com/paper/2510.21890/) (2025)
- [Erasing Undesirable Influence in Diffusion Models](https://mlsanity.com/paper/2401.05779/) (2024)
- [Direct Unlearning Optimization for Robust and Safe Text-to-Image Models](https://mlsanity.com/paper/2407.21035/) (2024)
- [O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions](https://mlsanity.com/paper/2409.18959/) (2024)
- [Constrained Learning with Non-Convex Losses](https://mlsanity.com/paper/2103.05134/) (2021)
- [Meta-Unlearning on Diffusion Models: Preventing Relearning Unlearned Concepts](https://mlsanity.com/paper/2410.12777/) (2024)
- [Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models](https://mlsanity.com/paper/2502.03607/) (2025)
- [Score Forgetting Distillation: A Swift, Data-Free Method for Machine Unlearning in Diffusion Models](https://mlsanity.com/paper/2409.11219/) (2024)
- [Constrained Diffusion Models via Dual Training](https://mlsanity.com/paper/2408.15094/) (2024)
- [Training-Free Constrained Generation With Stable Diffusion Models](https://mlsanity.com/paper/2502.05625/) (2025)
- [Data Unlearning in Diffusion Models](https://mlsanity.com/paper/2503.01034/) (2025)

## Built on by (most cited first, 2 of 2)

- [Mitigating Sequential Reappearance in Diffusion Data-Point Unlearning](https://mlsanity.com/paper/2609.25166/) (2026)
- [Data Unlearning via Inverse Distillation](https://mlsanity.com/paper/2609.36099/) (2026)

## Abstract (arXiv)

Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models -- two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained model, subject to explicit separation constraints from the unlearning distributions. Specifically, we formulate three constrained optimization problems based on reverse and forward KL divergences, and likelihood constraints. The first two generalize existing approaches for concept and data unlearning, while the third offers a novel and natural formulation for unlearning. Despite the nonconvexity of the KL constraints, we establish strong duality for all three problems, enabling us to explicitly characterize their optimal solutions as unlearning targets and develop primal-dual algorithms for each formulation. Experimental results demonstrate that our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines for concept and data unlearning, and that our likelihood-based approach matches unlearning effectiveness while better preserving retained concepts compared to baselines.