Avoid Catastrophic Forgetting with Rank-1 Fisher from Diffusion Models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911400840921088 |
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| author | Wang, Zekun Gupta, Anant Dong, Zihan MacLellan, Christopher J. |
| author_facet | Wang, Zekun Gupta, Anant Dong, Zihan MacLellan, Christopher J. |
| contents | Catastrophic forgetting remains a central obstacle for continual learning in neural models. Popular approaches -- replay and elastic weight consolidation (EWC) -- have limitations: replay requires a strong generator and is prone to distributional drift, while EWC implicitly assumes a shared optimum across tasks and typically uses a diagonal Fisher approximation. In this work, we study the gradient geometry of diffusion models, which can already produce high-quality replay data. We provide theoretical and empirical evidence that, in the low signal-to-noise ratio (SNR) regime, per-sample gradients become strongly collinear, yielding an empirical Fisher that is effectively rank-1 and aligned with the mean gradient. Leveraging this structure, we propose a rank-1 variant of EWC that is as cheap as the diagonal approximation yet captures the dominant curvature direction. We pair this penalty with a replay-based approach to encourage parameter sharing across tasks while mitigating drift. On class-incremental image generation datasets (MNIST, FashionMNIST, CIFAR-10, ImageNet-1k), our method consistently improves average FID and reduces forgetting relative to replay-only and diagonal-EWC baselines. In particular, forgetting is nearly eliminated on MNIST and FashionMNIST and is more than halved on ImageNet-1k. These results suggest that diffusion models admit an approximately rank-1 Fisher. With a better Fisher estimate, EWC becomes a strong complement to replay: replay encourages parameter sharing across tasks, while EWC effectively constrains replay-induced drift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Avoid Catastrophic Forgetting with Rank-1 Fisher from Diffusion Models Wang, Zekun Gupta, Anant Dong, Zihan MacLellan, Christopher J. Machine Learning Catastrophic forgetting remains a central obstacle for continual learning in neural models. Popular approaches -- replay and elastic weight consolidation (EWC) -- have limitations: replay requires a strong generator and is prone to distributional drift, while EWC implicitly assumes a shared optimum across tasks and typically uses a diagonal Fisher approximation. In this work, we study the gradient geometry of diffusion models, which can already produce high-quality replay data. We provide theoretical and empirical evidence that, in the low signal-to-noise ratio (SNR) regime, per-sample gradients become strongly collinear, yielding an empirical Fisher that is effectively rank-1 and aligned with the mean gradient. Leveraging this structure, we propose a rank-1 variant of EWC that is as cheap as the diagonal approximation yet captures the dominant curvature direction. We pair this penalty with a replay-based approach to encourage parameter sharing across tasks while mitigating drift. On class-incremental image generation datasets (MNIST, FashionMNIST, CIFAR-10, ImageNet-1k), our method consistently improves average FID and reduces forgetting relative to replay-only and diagonal-EWC baselines. In particular, forgetting is nearly eliminated on MNIST and FashionMNIST and is more than halved on ImageNet-1k. These results suggest that diffusion models admit an approximately rank-1 Fisher. With a better Fisher estimate, EWC becomes a strong complement to replay: replay encourages parameter sharing across tasks, while EWC effectively constrains replay-induced drift. |
| title | Avoid Catastrophic Forgetting with Rank-1 Fisher from Diffusion Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.23593 |