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Controllable Unlearning for Image-to-Image Generative Models via $\epsilon$-Constrained Optimization
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Proposes a controllable machine unlearning framework for image-to-image generative models that reformulates unlearning as an epsilon-constrained optimization solved by a gradient-based SQP-style method, yielding a Pareto front of solutions tunable via epsilon.
Problem
Machine unlearning in image-to-image generative models forces a single fixed trade-off between unlearning completeness on the forget set and utility on the retain set, with no theoretical convergence or Pareto guarantee.
Approach
Casts I2I unlearning as a bi-objective problem with the forget-set objective as an epsilon-constraint, solved by a gradient-based SQP variant with a control function; the two constraint boundaries define the valid epsilon range and each epsilon within it yields a Pareto optimal solution.
Key results
- On MAE with 50% center cropping, the highest-completeness boundary solution reaches forget-set FID 154.60 and IS 12.33 versus original 16.28 and 21.59, while retain-set IS 17.47 vs. original 21.83.
- Varying epsilon between the two boundaries yields a monotone trade-off: on MAE forget-set IS rises from 12.33 (highest) to 21.23 (lowest) while retain-set FID improves from 68.45 to 25.83.
- The paper reports its method outperforms Composite Loss on forget-set metrics in most model settings, though Composite Loss keeps retain-set utility better on some metrics.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use controllable unlearning at the highest-completeness boundary instead of the original model | MAE · Center crop 50%, forget set | IS: 21.59 -> 12.33 | Helped |
| Use controllable unlearning at the highest-completeness boundary instead of the original model | MAE · Center crop 50%, retain set | IS: 21.83 -> 17.47 | Hurt |
| Use controllable unlearning at the highest-completeness boundary instead of the original model | VQ-GAN · Center crop 50%, forget set | FID: 21.80 -> 139.21 | Helped |
| Use controllable unlearning at the highest-completeness boundary instead of the original model | Diffusion model · Center crop 50%, forget set | IS: 16.90 -> 11.84 | Helped |
| Increase ε from the highest-completeness boundary toward the lowest-unlearning boundary (ablation) | MAE · Center crop 50%, forget set | IS: 12.33 -> 17.93 -> 19.47 -> 20.68 -> 21.23 | Hurt |
| Increase ε from the highest-completeness boundary toward the lowest-unlearning boundary (ablation) | VQ-GAN · Center crop 50%, forget set | IS: 13.23 -> 14.14 -> 14.60 -> 15.20 -> 15.77 | Hurt |
| Increase ε from the highest-completeness boundary toward the lowest-unlearning boundary (ablation) | Diffusion model · Center crop 50%, forget set | IS: 11.84 -> 15.12 -> 15.92 -> 16.33 -> 16.36 | Hurt |
| Set Phase I control-function exponent δ to 2 (ablation) | Controllable unlearning framework · Phase I convergence | convergence rate | Helped |
| Set Phase II control-function exponent δ to 1 (ablation) | Controllable unlearning framework · Phase II convergence | convergence rate | Helped |
Surprising findings
- Pareto optimality guarantees rely on convexity assumptions, which the authors acknowledge do not hold for deep networks; non-convex cases give only weak Pareto optimality or Pareto stability.
Limitations
- Pareto optimality guarantees assume convexity of objectives and feasible set, which deep networks do not satisfy; only weak Pareto optimality holds otherwise.
- Divergence is approximated by L2 loss surrogate, not exact KL.
- Evaluated only on center-cropping/inpainting-style I2I tasks with two datasets and three model families.
Experimental setup
Datasets: ImageNet-1K Places-365
Benchmarks: ImageNet-1K Places-365
Metrics: Inception Score FID CLIP embedding cosine similarity
Baselines: Max Loss Retain Label Noisy Label Composite Loss
Builds on: SQP composite loss unlearning Pareto optimality
Closest papers by meaning
- Machine Unlearning for Image-to-Image Generative Models (ICLR 2024 · similarity 0.92)
- Generative Unlearning for Any Identity (CVPR 2024 · similarity 0.89)
- Boosting Alignment for Post-Unlearning Text-to-Image Generative Models (NeurIPS 2024 · similarity 0.89)
- Enabling Preference-driven Unlearning in Few-step Distilled Text-to-Image Diffusion Models (NeurIPS 2026 · similarity 0.88)
- The Illusion of Unlearning: The Unstable Nature of Machine Unlearning in Text-to-Image Diffusion Models (CVPR 2025 · similarity 0.87)
- Score Forgetting Distillation: A Swift, Data-Free Method for Machine Unlearning in Diffusion Models (ICLR 2025 · similarity 0.87)
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